Your selections:

19Bagirov, Adil
15Sukhorukova, Nadezda
12Pineda-Villavicencio, Guillermo
11Rubinov, Alex
10Yost, David
7Stranieri, Andrew
7Webb, Dean
6Kouhbor, Shahnaz
6Kruger, Alexander
4Kulkarni, Pradnya
3Bui, Hoa
3Mammadov, Musa
3Mirzayeva, Hijran
3Mittal, Manish
3Tian, Jing
3Vamplew, Peter
3Wu, Zhiyou
2Amiel, Hélène
2Beliakov, Gleb

Show More

Show Less

150103 Numerical and Computational Mathematics
140102 Applied Mathematics
12Nonsmooth optimization
110802 Computation Theory and Mathematics
80101 Pure Mathematics
6Chebyshev approximation
54901 Applied mathematics
54904 Pure mathematics
5Classification
5Data mining
5Global optimization
5Optimisation
40801 Artificial Intelligence and Image Processing
40906 Electrical and Electronic Engineering
4Discrete gradient method
4Nonconvex optimization
4Optimization
4WLAN
4Wireless
3Cluster analysis

Show More

Show Less

Format Type

New algorithm to find a shape of a finite set of points

- Sukhorukova, Nadezda, Ugon, Julien

**Authors:**Sukhorukova, Nadezda , Ugon, Julien**Date:**2003**Type:**Text , Conference paper**Relation:**Paper presented at the Symposium on Industrial Optimisation and the 9th Australian Optimisation Day, Perth : 30th September, 2002**Full Text:****Reviewed:****Description:**Very often in data classification problems we have to determine a shape of a finite set of points within datasets. One of the most common approaches to represent such sets is to determine them as collections of several groups of points. The goal of this project is to develop some algorithms to find a shape for each group. Numerical experiments using the Discrete Gradient method have been done. The results are presented.**Description:**E1**Description:**2003000351

**Authors:**Sukhorukova, Nadezda , Ugon, Julien**Date:**2003**Type:**Text , Conference paper**Relation:**Paper presented at the Symposium on Industrial Optimisation and the 9th Australian Optimisation Day, Perth : 30th September, 2002**Full Text:****Reviewed:****Description:**Very often in data classification problems we have to determine a shape of a finite set of points within datasets. One of the most common approaches to represent such sets is to determine them as collections of several groups of points. The goal of this project is to develop some algorithms to find a shape for each group. Numerical experiments using the Discrete Gradient method have been done. The results are presented.**Description:**E1**Description:**2003000351

Patient admission prediction using a pruned fuzzy min-max neural network with rule extraction

- Wang, Jin, Lim, Cheepeng, Creighton, Douglas, Khorsavi, Abbas, Nahavandi, Saeid, Ugon, Julien, Vamplew, Peter, Stranieri, Andrew, Martin, Laura, Freischmidt, Anton

**Authors:**Wang, Jin , Lim, Cheepeng , Creighton, Douglas , Khorsavi, Abbas , Nahavandi, Saeid , Ugon, Julien , Vamplew, Peter , Stranieri, Andrew , Martin, Laura , Freischmidt, Anton**Date:**2015**Type:**Text , Journal article**Relation:**Neural Computing and Applications Vol. 26, no. 2 (2015), p. 277-289**Full Text:**false**Reviewed:****Description:**A useful patient admission prediction model that helps the emergency department of a hospital admit patients efficiently is of great importance. It not only improves the care quality provided by the emergency department but also reduces waiting time of patients. This paper proposes an automatic prediction method for patient admission based on a fuzzy minâ€“max neural network (FMM) with rules extraction. The FMM neural network forms a set of hyperboxes by learning through data samples, and the learned knowledge is used for prediction. In addition to providing predictions, decision rules are extracted from the FMM hyperboxes to provide an explanation for each prediction. In order to simplify the structure of FMM and the decision rules, an optimization method that simultaneously maximizes prediction accuracy and minimizes the number of FMM hyperboxes is proposed. Specifically, a genetic algorithm is formulated to find the optimal configuration of the decision rules. The experimental results using a large data set consisting of 450740 real patient records reveal that the proposed method achieves comparable or even better prediction accuracy than state-of-the-art classifiers with the additional ability to extract a set of explanatory rules to justify its predictions.

Visual character N-grams for classification and retrieval of radiological images

- Kulkarni, Pradnya, Stranieri, Andrew, Kulkarni, Siddhivinayak, Ugon, Julien, Mittal, Manish

**Authors:**Kulkarni, Pradnya , Stranieri, Andrew , Kulkarni, Siddhivinayak , Ugon, Julien , Mittal, Manish**Date:**2014**Type:**Text , Journal article**Relation:**International Journal of Multimedia & Its Applications Vol. 6, no. 2 (April 2014), p. 35-49**Full Text:****Reviewed:****Description:**Diagnostic radiology struggles to maintain high interpretation accuracy. Retrieval of past similar cases would help the inexperienced radiologist in the interpretation process. Character n-gram model has been effective in text retrieval context in languages such as Chinese where there are no clear word boundaries. We propose the use of visual character n-gram model for representation of image for classification and retrieval purposes. Regions of interests in mammographic images are represented with the character n-gram features. These features are then used as input to back-propagation neural network for classification of regions into normal and abnormal categories. Experiments on miniMIAS database show that character n-gram features are useful in classifying the regions into normal and abnormal categories. Promising classification accuracies are observed (83.33%) for fatty background tissue warranting further investigation. We argue that Classifying regions of interests would reduce the number of comparisons necessary for finding similar images from the database and hence would reduce the time required for retrieval of past similar cases.

**Authors:**Kulkarni, Pradnya , Stranieri, Andrew , Kulkarni, Siddhivinayak , Ugon, Julien , Mittal, Manish**Date:**2014**Type:**Text , Journal article**Relation:**International Journal of Multimedia & Its Applications Vol. 6, no. 2 (April 2014), p. 35-49**Full Text:****Reviewed:****Description:**Diagnostic radiology struggles to maintain high interpretation accuracy. Retrieval of past similar cases would help the inexperienced radiologist in the interpretation process. Character n-gram model has been effective in text retrieval context in languages such as Chinese where there are no clear word boundaries. We propose the use of visual character n-gram model for representation of image for classification and retrieval purposes. Regions of interests in mammographic images are represented with the character n-gram features. These features are then used as input to back-propagation neural network for classification of regions into normal and abnormal categories. Experiments on miniMIAS database show that character n-gram features are useful in classifying the regions into normal and abnormal categories. Promising classification accuracies are observed (83.33%) for fatty background tissue warranting further investigation. We argue that Classifying regions of interests would reduce the number of comparisons necessary for finding similar images from the database and hence would reduce the time required for retrieval of past similar cases.

Chebyshev multivariate polynomial approximation and point reduction procedure

- Sukhorukova, Nadezda, Ugon, Julien, Yost, David

**Authors:**Sukhorukova, Nadezda , Ugon, Julien , Yost, David**Date:**2021**Type:**Text , Journal article**Relation:**Constructive Approximation Vol. 53, no. 3 (2021), p. 529-544**Relation:**http://purl.org/au-research/grants/arc/DP180100602**Full Text:****Reviewed:****Description:**We apply the methods of nonsmooth and convex analysis to extend the study of Chebyshev (uniform) approximation for univariate polynomial functions to the case of general multivariate functions (not just polynomials). First of all, we give new necessary and sufficient optimality conditions for multivariate approximation, and a geometrical interpretation of them which reduces to the classical alternating sequence condition in the univariate case. Then, we present a procedure for verification of necessary and sufficient optimality conditions that is based on our generalization of the notion of alternating sequence to the case of multivariate polynomials. Finally, we develop an algorithm for fast verification of necessary optimality conditions in the multivariate polynomial case. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

**Authors:**Sukhorukova, Nadezda , Ugon, Julien , Yost, David**Date:**2021**Type:**Text , Journal article**Relation:**Constructive Approximation Vol. 53, no. 3 (2021), p. 529-544**Relation:**http://purl.org/au-research/grants/arc/DP180100602**Full Text:****Reviewed:****Description:**We apply the methods of nonsmooth and convex analysis to extend the study of Chebyshev (uniform) approximation for univariate polynomial functions to the case of general multivariate functions (not just polynomials). First of all, we give new necessary and sufficient optimality conditions for multivariate approximation, and a geometrical interpretation of them which reduces to the classical alternating sequence condition in the univariate case. Then, we present a procedure for verification of necessary and sufficient optimality conditions that is based on our generalization of the notion of alternating sequence to the case of multivariate polynomials. Finally, we develop an algorithm for fast verification of necessary optimality conditions in the multivariate polynomial case. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Detecting K-complexes for sleep stage identification using nonsmooth optimization

- Moloney, David, Sukhorukova, Nadezda, Vamplew, Peter, Ugon, Julien, Li, Gang, Beliakov, Gleb, Philippe, Carole, Amiel, Hélène, Ugon, Adrien

**Authors:**Moloney, David , Sukhorukova, Nadezda , Vamplew, Peter , Ugon, Julien , Li, Gang , Beliakov, Gleb , Philippe, Carole , Amiel, Hélène , Ugon, Adrien**Date:**2012**Type:**Text , Journal article**Relation:**ANZIAM Journal Vol. 52, no. 4 (2012), p. 319-332**Full Text:****Reviewed:****Description:**The process of sleep stage identification is a labour-intensive task that involves the specialized interpretation of the polysomnographic signals captured from a patient's overnight sleep session. Automating this task has proven to be challenging for data mining algorithms because of noise, complexity and the extreme size of data. In this paper we apply nonsmooth optimization to extract key features that lead to better accuracy. We develop a specific procedure for identifying K-complexes, a special type of brain wave crucial for distinguishing sleep stages. The procedure contains two steps. We first extract "easily classified" K-complexes, and then apply nonsmooth optimization methods to extract features from the remaining data and refine the results from the first step. Numerical experiments show that this procedure is efficient for detecting K-complexes. It is also found that most classification methods perform significantly better on the extracted features. © 2012 Australian Mathematical Society.

**Authors:**Moloney, David , Sukhorukova, Nadezda , Vamplew, Peter , Ugon, Julien , Li, Gang , Beliakov, Gleb , Philippe, Carole , Amiel, Hélène , Ugon, Adrien**Date:**2012**Type:**Text , Journal article**Relation:**ANZIAM Journal Vol. 52, no. 4 (2012), p. 319-332**Full Text:****Reviewed:****Description:**The process of sleep stage identification is a labour-intensive task that involves the specialized interpretation of the polysomnographic signals captured from a patient's overnight sleep session. Automating this task has proven to be challenging for data mining algorithms because of noise, complexity and the extreme size of data. In this paper we apply nonsmooth optimization to extract key features that lead to better accuracy. We develop a specific procedure for identifying K-complexes, a special type of brain wave crucial for distinguishing sleep stages. The procedure contains two steps. We first extract "easily classified" K-complexes, and then apply nonsmooth optimization methods to extract features from the remaining data and refine the results from the first step. Numerical experiments show that this procedure is efficient for detecting K-complexes. It is also found that most classification methods perform significantly better on the extracted features. © 2012 Australian Mathematical Society.

Nonsmooth optimization algorithm for solving clusterwise linear regression problems

- Bagirov, Adil, Ugon, Julien, Mirzayeva, Hijran

**Authors:**Bagirov, Adil , Ugon, Julien , Mirzayeva, Hijran**Date:**2015**Type:**Text , Journal article**Relation:**Journal of Optimization Theory and Applications Vol. 164, no. 3 (2015), p. 755-780**Relation:**http://purl.org/au-research/grants/arc/DP140103213**Full Text:**false**Reviewed:****Description:**Clusterwise linear regression consists of finding a number of linear regression functions each approximating a subset of the data. In this paper, the clusterwise linear regression problem is formulated as a nonsmooth nonconvex optimization problem and an algorithm based on an incremental approach and on the discrete gradient method of nonsmooth optimization is designed to solve it. This algorithm incrementally divides the whole dataset into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate good starting points for solving global optimization problems at each iteration of the incremental algorithm. The algorithm is compared with the multi-start Spath and the incremental algorithms on several publicly available datasets for regression analysis.

Generalised rational approximation and its application to improve deep learning classifiers

- Peiris, V, Sharon, Nir, Sukhorukova, Nadezda, Ugon, Julien

**Authors:**Peiris, V , Sharon, Nir , Sukhorukova, Nadezda , Ugon, Julien**Date:**2021**Type:**Text , Journal article**Relation:**Applied Mathematics and Computation Vol. 389, no. (2021), p.**Relation:**https://purl.org/au-research/grants/arc/DP180100602**Full Text:**false**Reviewed:****Description:**A rational approximation (that is, approximation by a ratio of two polynomials) is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non-Lipschitz functions, where polynomial approximations are not efficient. We prove that the optimisation problems appearing in the best uniform rational approximation and its generalisation to a ratio of linear combinations of basis functions are quasiconvex even when the basis functions are not restricted to monomials. Then we show how this fact can be used in the development of computational methods. This paper presents a theoretical study of the arising optimisation problems and provides results of several numerical experiments. We apply our approximation as a preprocessing step to deep learning classifiers and demonstrate that the classification accuracy is significantly improved compared to the classification of the raw signals. © 2020**Description:**This research was supported by the Australian Research Council (ARC), Solving hard Chebyshev approximation problems through nonsmooth analysis (Discovery Project DP180100602 ). This research was partially sponsored by Tel Aviv-Swinburne Research Collaboration Grant (2019).

Classification through incremental max-min separability

- Bagirov, Adil, Ugon, Julien, Webb, Dean, Karasozen, Bulent

**Authors:**Bagirov, Adil , Ugon, Julien , Webb, Dean , Karasozen, Bulent**Date:**2011**Type:**Text , Journal article**Relation:**Pattern Analysis and Applications Vol. 14, no. 2 (2011), p. 165-174**Relation:**http://purl.org/au-research/grants/arc/DP0666061**Full Text:**false**Reviewed:****Description:**Piecewise linear functions can be used to approximate non-linear decision boundaries between pattern classes. Piecewise linear boundaries are known to provide efficient real-time classifiers. However, they require a long training time. Finding piecewise linear boundaries between sets is a difficult optimization problem. Most approaches use heuristics to avoid solving this problem, which may lead to suboptimal piecewise linear boundaries. In this paper, we propose an algorithm for globally training hyperplanes using an incremental approach. Such an approach allows one to find a near global minimizer of the classification error function and to compute as few hyperplanes as needed for separating sets. We apply this algorithm for solving supervised data classification problems and report the results of numerical experiments on real-world data sets. These results demonstrate that the new algorithm requires a reasonable training time and its test set accuracy is consistently good on most data sets compared with mainstream classifiers. © 2010 Springer-Verlag London Limited.

An algorithm for minimizing clustering functions

**Authors:**Bagirov, Adil , Ugon, Julien**Date:**2005**Type:**Text , Journal article**Relation:**Optimization Vol. 54, no. 4-5 (Aug-Oct 2005), p. 351-368**Full Text:****Reviewed:****Description:**The problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization. An algorithm for solving the latter optimization problem is developed which allows one to significantly reduce the computational efforts. This algorithm is based on the so-called discrete gradient method. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed algorithm.**Description:**C1**Description:**2003001266

**Authors:**Bagirov, Adil , Ugon, Julien**Date:**2005**Type:**Text , Journal article**Relation:**Optimization Vol. 54, no. 4-5 (Aug-Oct 2005), p. 351-368**Full Text:****Reviewed:****Description:**The problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization. An algorithm for solving the latter optimization problem is developed which allows one to significantly reduce the computational efforts. This algorithm is based on the so-called discrete gradient method. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed algorithm.**Description:**C1**Description:**2003001266

Optimality conditions and optimization methods for quartic polynomial optimization

- Wu, Zhiyou, Tian, Jing, Quan, Jing, Ugon, Julien

**Authors:**Wu, Zhiyou , Tian, Jing , Quan, Jing , Ugon, Julien**Date:**2014**Type:**Text , Journal article**Relation:**Applied Mathematics and Computation Vol. 232, no. (2014), p. 968-982**Full Text:**false**Reviewed:****Description:**In this paper multivariate quartic polynomial optimization program (QPOP) is considered. Quartic optimization problems arise in various practical applications and are proved to be NP hard. We discuss necessary global optimality conditions for quartic problem (QPOP). And then we present a new (strongly or ε-strongly) local optimization method according to necessary global optimality conditions, which may escape and improve some KKT points. Finally we design a global optimization method for problem (QPOP) by combining the new (strongly or ε-strongly) local optimization method and an auxiliary function. Numerical examples show that our algorithms are efficient and stable.

Connectivity of cubical polytopes

- Bui, Hoa, Pineda-Villavicencio, Guillermo, Ugon, Julien

**Authors:**Bui, Hoa , Pineda-Villavicencio, Guillermo , Ugon, Julien**Date:**2019**Type:**Text , Journal article**Relation:**Journal of Combinatorial Theory Series A Vol. 169, no. (Jan 2019), p. 21**Full Text:****Reviewed:****Description:**A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. We deal with the connectivity of the graphs of cubical polytopes. We first establish that, for any d >= 3, the graph of a cubical d-polytope with minimum degree 5 is min{delta, 2d - 2}-connected. Second, we show, for any d >= 4, that every minimum separator of cardinality at most 2d - 3 in such a graph consists of all the neighbours of some vertex and that removing the vertices of the separator from the graph leaves exactly two components, with one of them being the vertex itself. (C) 2019 Elsevier Inc. All rights reserved.

**Authors:**Bui, Hoa , Pineda-Villavicencio, Guillermo , Ugon, Julien**Date:**2019**Type:**Text , Journal article**Relation:**Journal of Combinatorial Theory Series A Vol. 169, no. (Jan 2019), p. 21**Full Text:****Reviewed:****Description:**A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. We deal with the connectivity of the graphs of cubical polytopes. We first establish that, for any d >= 3, the graph of a cubical d-polytope with minimum degree 5 is min{delta, 2d - 2}-connected. Second, we show, for any d >= 4, that every minimum separator of cardinality at most 2d - 3 in such a graph consists of all the neighbours of some vertex and that removing the vertices of the separator from the graph leaves exactly two components, with one of them being the vertex itself. (C) 2019 Elsevier Inc. All rights reserved.

Optimization solvers and problem formulations for solving data clustering problems

**Authors:**Ugon, Julien**Date:**2007**Type:**Text , Journal article**Relation:**Pacific Journal of Optimization Vol. 3, no. 2 (2007), p. 387-397**Full Text:**false**Reviewed:****Description:**A popular apprach for solving complex optimization problems is through relaxation: some constraints are removed in order to have a convex problem approximating the original problem. On the other hand, direct approaches for solving such problems are becoming increasingly powerful. This paper examines two cases drawn from data analysis, in order to compare the two techniques.**Description:**C1**Description:**2003004937

Nonsmooth nonconvex optimization approach to clusterwise linear regression problems

- Bagirov, Adil, Ugon, Julien, Mirzayeva, Hijran

**Authors:**Bagirov, Adil , Ugon, Julien , Mirzayeva, Hijran**Date:**2013**Type:**Text , Journal article**Relation:**European Journal of Operational Research Vol. 229, no. 1 (2013), p. 132-142**Full Text:**false**Reviewed:****Description:**Clusterwise regression consists of finding a number of regression functions each approximating a subset of the data. In this paper, a new approach for solving the clusterwise linear regression problems is proposed based on a nonsmooth nonconvex formulation. We present an algorithm for minimizing this nonsmooth nonconvex function. This algorithm incrementally divides the whole data set into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate a good starting point for solving global optimization problems at each iteration of the incremental algorithm. Such an approach allows one to find global or near global solution to the problem when the data sets are sufficiently dense. The algorithm is compared with the multistart Späth algorithm on several publicly available data sets for regression analysis. © 2013 Elsevier B.V. All rights reserved.**Description:**2003011018

Texture image classification using pixel N-grams

- Kulkarni, Pradnya, Stranieri, Andrew, Ugon, Julien

**Authors:**Kulkarni, Pradnya , Stranieri, Andrew , Ugon, Julien**Date:**2016**Type:**Text , Conference proceedings**Relation:**2016 IEEE International Conference on Signal and Image Processing (ICSIP); Beijing, China; 13-15 Aug, 2016 p. 137-141**Full Text:**false**Reviewed:****Description:**Various statistical methods such as co-occurrence matrix, local binary patterns and spectral approaches such as Gabor filters have been used for generating global features for image classification. However, global image features fail to distinguish between local variations within an image. Bag-of-visual-words (BoVW) model do capture local variations in an image, but typically do not consider spatial relationships between the visual words. Here, a novel image representation ‘Pixel N-grams’, inspired from the character N-gram concept in text retrieval has been applied for texture classification purpose. Texture is an important property for image classification. Experiments on the benchmark texture database (UIUC) demonstrates that the overall classification accuracy resulting from Pixel N-gram approach (89.5%) is comparable with that achieved using BoVW approach (84.4%) with the added advantage of simplicity and reduced computational cost.

Linkedness of cartesian products of complete graphs

- Jorgensen, Leif, Pineda-Villavicencio, Guillermo, Ugon, Julien

**Authors:**Jorgensen, Leif , Pineda-Villavicencio, Guillermo , Ugon, Julien**Date:**2022**Type:**Text , Journal article**Relation:**Ars Mathematica Contemporanea Vol. 22, no. 2 (2022), p.**Relation:**http://purl.org/au-research/grants/arc/DP180100602**Full Text:****Reviewed:****Description:**This paper is concerned with the linkedness of Cartesian products of complete graphs. A graph with at least 2k vertices is k-linked if, for every set of 2k distinct vertices organised in arbitrary k pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We show that the Cartesian product Kd1+1 × Kd2+1 of complete graphs Kd1+1 and Kd2+1 is

**Authors:**Jorgensen, Leif , Pineda-Villavicencio, Guillermo , Ugon, Julien**Date:**2022**Type:**Text , Journal article**Relation:**Ars Mathematica Contemporanea Vol. 22, no. 2 (2022), p.**Relation:**http://purl.org/au-research/grants/arc/DP180100602**Full Text:****Reviewed:****Description:**This paper is concerned with the linkedness of Cartesian products of complete graphs. A graph with at least 2k vertices is k-linked if, for every set of 2k distinct vertices organised in arbitrary k pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We show that the Cartesian product Kd1+1 × Kd2+1 of complete graphs Kd1+1 and Kd2+1 is

Piecewise partially separable functions and a derivative-free algorithm for large scale nonsmooth optimization

**Authors:**Bagirov, Adil , Ugon, Julien**Date:**2006**Type:**Text , Journal article**Relation:**Journal of Global Optimization Vol. 35, no. 2 (Jun 2006), p. 163-195**Full Text:****Reviewed:****Description:**This paper introduces the notion of piecewise partially separable functions and studies their properties. We also consider some of many applications of these functions. Finally, we consider the problem of minimizing of piecewise partially separable functions and develop an algorithm for its solution. This algorithm exploits the structure of such functions. We present the results of preliminary numerical experiments.**Description:**2003001532

**Authors:**Bagirov, Adil , Ugon, Julien**Date:**2006**Type:**Text , Journal article**Relation:**Journal of Global Optimization Vol. 35, no. 2 (Jun 2006), p. 163-195**Full Text:****Reviewed:****Description:**This paper introduces the notion of piecewise partially separable functions and studies their properties. We also consider some of many applications of these functions. Finally, we consider the problem of minimizing of piecewise partially separable functions and develop an algorithm for its solution. This algorithm exploits the structure of such functions. We present the results of preliminary numerical experiments.**Description:**2003001532

The linkedness of cubical polytopes : beyond the cube

- Bui, Hoa, Pineda-Villavicencio, Guillermo, Ugon, Julien

**Authors:**Bui, Hoa , Pineda-Villavicencio, Guillermo , Ugon, Julien**Date:**2024**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 347, no. 3 (2024), p.**Relation:**https://purl.org/au-research/grants/arc/DP180100602**Full Text:****Reviewed:****Description:**A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. In a previous paper [3] we proved that every cubical d-polytope is ⌊d/2⌋-linked. Here we strengthen this result by establishing the ⌊(d+1)/2⌋-linkedness of cubical d-polytopes, for every d≠3. A graph G is strongly k-linked if it has at least 2k+1 vertices and, for every vertex v of G, the subgraph G−v is k-linked. We say that a polytope is (strongly) k-linked if its graph is (strongly) k-linked. In this paper, we also prove that every cubical d-polytope is strongly ⌊d/2⌋-linked, for every d≠3. These results are best possible for this class of polytopes.**Description:**A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. In a previous paper [3] we proved that every cubical d-polytope is

**Authors:**Bui, Hoa , Pineda-Villavicencio, Guillermo , Ugon, Julien**Date:**2024**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 347, no. 3 (2024), p.**Relation:**https://purl.org/au-research/grants/arc/DP180100602**Full Text:****Reviewed:****Description:**A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. In a previous paper [3] we proved that every cubical d-polytope is ⌊d/2⌋-linked. Here we strengthen this result by establishing the ⌊(d+1)/2⌋-linkedness of cubical d-polytopes, for every d≠3. A graph G is strongly k-linked if it has at least 2k+1 vertices and, for every vertex v of G, the subgraph G−v is k-linked. We say that a polytope is (strongly) k-linked if its graph is (strongly) k-linked. In this paper, we also prove that every cubical d-polytope is strongly ⌊d/2⌋-linked, for every d≠3. These results are best possible for this class of polytopes.**Description:**A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. In a previous paper [3] we proved that every cubical d-polytope is

Facility location via continuous optimization with discontinuous objective functions

- Ugon, Julien, Kouhbor, Shahnaz, Mammadov, Musa, Rubinov, Alex, Kruger, Alexander

**Authors:**Ugon, Julien , Kouhbor, Shahnaz , Mammadov, Musa , Rubinov, Alex , Kruger, Alexander**Date:**2007**Type:**Text , Journal article**Relation:**ANZIAM Journal Vol. 48, no. 3 (2007), p. 315-325**Full Text:****Reviewed:****Description:**Facility location problems are one of the most common applications of optimization methods. Continuous formulations are usually more accurate, but often result in complex problems that cannot be solved using traditional optimization methods. This paper examines the use of a global optimization method - AGOP - for solving location problems where the objective function is discontinuous. This approach is motivated by a real-world application in wireless networks design. © Australian Mathematical Society 2007.**Description:**2003004859

**Authors:**Ugon, Julien , Kouhbor, Shahnaz , Mammadov, Musa , Rubinov, Alex , Kruger, Alexander**Date:**2007**Type:**Text , Journal article**Relation:**ANZIAM Journal Vol. 48, no. 3 (2007), p. 315-325**Full Text:****Reviewed:****Description:**Facility location problems are one of the most common applications of optimization methods. Continuous formulations are usually more accurate, but often result in complex problems that cannot be solved using traditional optimization methods. This paper examines the use of a global optimization method - AGOP - for solving location problems where the objective function is discontinuous. This approach is motivated by a real-world application in wireless networks design. © Australian Mathematical Society 2007.**Description:**2003004859

Characterization theorem for best linear spline approximation with free knots

- Sukhorukova, Nadezda, Ugon, Julien

**Authors:**Sukhorukova, Nadezda , Ugon, Julien**Date:**2010**Type:**Text , Journal article**Relation:**Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Vol. 17, no. 5 (2010), p. 687-708**Full Text:**false**Reviewed:****Description:**A necessary condition for a best Chebyshev approximation by piecewise linear functions is derived using quasidifferential calculus. We first discover some properties of the knots joining the linear functions. Then we use these properties to obtain the optimality condition. This condition is stronger than existing results. We present an example of linear spline approximation where the existing optimality conditions are satisfied, but not the proposed one, which shows that it is not optimal. Copyright Â© 2010 Watam Press.

Classes and clusters in data analysis

- Rubinov, Alex, Sukhorukova, Nadezda, Ugon, Julien

**Authors:**Rubinov, Alex , Sukhorukova, Nadezda , Ugon, Julien**Date:**2006**Type:**Text , Journal article**Relation:**European Journal of Operational Research Vol. 173, no. 3 (Sep 2006), p. 849-865**Full Text:****Reviewed:****Description:**We discuss the relation between classes and clusters in datasets with given classes. We examine the distribution of classes within obtained clusters, using different clustering methods which are based on different techniques. We also study the structure of the obtained clusters. One of the main conclusions, obtained in this research is that the notion purity cannot be always used for evaluation of accuracy of clustering techniques. (c) 2005 Elsevier B.V. All rights reserved.**Description:**C1**Description:**2003001593

**Authors:**Rubinov, Alex , Sukhorukova, Nadezda , Ugon, Julien**Date:**2006**Type:**Text , Journal article**Relation:**European Journal of Operational Research Vol. 173, no. 3 (Sep 2006), p. 849-865**Full Text:****Reviewed:****Description:**We discuss the relation between classes and clusters in datasets with given classes. We examine the distribution of classes within obtained clusters, using different clustering methods which are based on different techniques. We also study the structure of the obtained clusters. One of the main conclusions, obtained in this research is that the notion purity cannot be always used for evaluation of accuracy of clustering techniques. (c) 2005 Elsevier B.V. All rights reserved.**Description:**C1**Description:**2003001593

Are you sure you would like to clear your session, including search history and login status?