Aggregate subgradient method for nonsmooth DC optimization
- Authors: Bagirov, Adil , Taheri, Sona , Joki, Kaisa , Karmitsa, Napsu , Mäkelä, Marko
- Date: 2021
- Type: Text , Journal article
- Relation: Optimization Letters Vol. 15, no. 1 (2021), p. 83-96
- Relation: http://purl.org/au-research/grants/arc/DP190100580
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- Description: The aggregate subgradient method is developed for solving unconstrained nonsmooth difference of convex (DC) optimization problems. The proposed method shares some similarities with both the subgradient and the bundle methods. Aggregate subgradients are defined as a convex combination of subgradients computed at null steps between two serious steps. At each iteration search directions are found using only two subgradients: the aggregate subgradient and a subgradient computed at the current null step. It is proved that the proposed method converges to a critical point of the DC optimization problem and also that the number of null steps between two serious steps is finite. The new method is tested using some academic test problems and compared with several other nonsmooth DC optimization solvers. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
Bundle methods for nonsmooth DC optimization
- Authors: Joki, Kaisa , Bagirov, Adil
- Date: 2020
- Type: Text , Book chapter
- Relation: Numerical Nonsmooth Optimization: State of the Art Algorithms Chapter 8 p. 263-296
- Full Text: false
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- Description: This chapter is devoted to algorithms for solving nonsmooth unconstrained difference of convex optimization problems. Different types of stationarity conditions are discussed and the relationship between sets of different stationary points (critical, Clarke stationary and inf-stationary) is established. Bundle methods are developed based on a nonconvex piecewise linear model of the objective function and the convergence of these methods is studied. Numerical results are presented to demonstrate the performance of the methods. © Springer Nature Switzerland AG 2020.
Clusterwise support vector linear regression
- Authors: Joki, Kaisa , Bagirov, Adil , Karmitsa, Napsu , Mäkelä, Marko , Taheri, Sona
- Date: 2020
- Type: Text , Journal article
- Relation: European Journal of Operational Research Vol. 287, no. 1 (2020), p. 19-35
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- Description: In clusterwise linear regression (CLR), the aim is to simultaneously partition data into a given number of clusters and to find regression coefficients for each cluster. In this paper, we propose a novel approach to model and solve the CLR problem. The main idea is to utilize the support vector machine (SVM) approach to model the CLR problem by using the SVM for regression to approximate each cluster. This new formulation of the CLR problem is represented as an unconstrained nonsmooth optimization problem, where we minimize a difference of two convex (DC) functions. To solve this problem, a method based on the combination of the incremental algorithm and the double bundle method for DC optimization is designed. Numerical experiments are performed to validate the reliability of the new formulation for CLR and the efficiency of the proposed method. The results show that the SVM approach is suitable for solving CLR problems, especially, when there are outliers in data. © 2020 Elsevier B.V.
- Description: Funding details: Academy of Finland, 289500, 294002, 319274 Funding details: Turun Yliopisto Funding details: Australian Research Council, ARC, (Project no. DP190100580 ).
Double bundle method for finding clarke stationary points in nonsmooth dc programming
- Authors: Joki, Kaisa , Bagirov, Adil , Karmitsa, Napsu , Makela, Marko , Taheri, Sona
- Date: 2018
- Type: Text , Journal article
- Relation: SIAM Journal on Optimization Vol. 28, no. 2 (2018), p. 1892-1919
- Relation: http://purl.org/au-research/grants/arc/DP140103213
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- Description: The aim of this paper is to introduce a new proximal double bundle method for unconstrained nonsmooth optimization, where the objective function is presented as a difference of two convex (DC) functions. The novelty in our method is a new escape procedure which enables us to guarantee approximate Clarke stationarity for solutions by utilizing the DC components of the objective function. This optimality condition is stronger than the criticality condition typically used in DC programming. Moreover, if a candidate solution is not approximate Clarke stationary, then the escape procedure returns a descent direction. With this escape procedure, we can avoid some shortcomings encountered when criticality is used. The finite termination of the double bundle method to an approximate Clarke stationary point is proved by assuming that the subdifferentials of DC components are polytopes. Finally, some encouraging numerical results are presented.
Limited Memory Bundle Method for Clusterwise Linear Regression
- Authors: Karmitsa, Napsu , Bagirov, Adil , Taheri, Sona , Joki, Kaisa
- Date: 2022
- Type: Text , Book chapter
- Relation: Intelligent Systems, Control and Automation: Science and Engineering p. 109-122
- Relation: http://purl.org/au-research/grants/arc/DP190100580
- Full Text: false
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- Description: A clusterwise linear regression problem consists of finding a number of linear functions each approximating a subset of the given data. In this paper, the limited memory bundle method is modified and combined with the incremental approach to solve this problem using its nonsmooth optimization formulation. The main contribution of the proposed method is to obtain a fast solution time for large-scale clusterwise linear regression problems. The proposed algorithm is tested on small and large real-world data sets and compared with other algorithms for clusterwise linear regression. Numerical results demonstrate that the proposed algorithm is especially efficient in data sets with large numbers of data points and input variables. © 2022, Springer Nature Switzerland AG.
A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes
- Authors: Joki, Kaisa , Bagirov, Adil , Karmitsa, Napsu , Makela, Marko
- Date: 2017
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 68, no. 3 (2017), p. 501-535
- Relation: http://purl.org/au-research/grants/arc/DP140103213
- Full Text: false
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- Description: In this paper, we develop a version of the bundle method to solve unconstrained difference of convex (DC) programming problems. It is assumed that a DC representation of the objective function is available. Our main idea is to utilize subgradients of both the first and second components in the DC representation. This subgradient information is gathered from some neighborhood of the current iteration point and it is used to build separately an approximation for each component in the DC representation. By combining these approximations we obtain a new nonconvex cutting plane model of the original objective function, which takes into account explicitly both the convex and the concave behavior of the objective function. We design the proximal bundle method for DC programming based on this new approach and prove the convergence of the method to an -critical point. The algorithm is tested using some academic test problems and the preliminary numerical results have shown the good performance of the new bundle method. An interesting fact is that the new algorithm finds nearly always the global solution in our test problems.
Preface of the special issue OR: Connecting sciences supported by global optimization related to the 25th European conference on operational research (EURO XXV 2012)
- Authors: Bagirov, Adil , Miettinen, Kaisa , Weber, Gerhard-Wilhelm
- Date: 2014
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 60, no. 1 (June 2014), p. 1-3
- Full Text: false
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- Description: C1
Nonsmooth optimization-based hyperparameter-free neural networks for large-scale regression
- Authors: Karmitsa, Napsu , Taheri, Sona , Joki, Kaisa , Paasivirta, Pauliina , Defterdarovic, J. , Bagirov, Adil , Mäkelä, Marko
- Date: 2023
- Type: Text , Journal article
- Relation: Algorithms Vol. 16, no. 9 (2023), p.
- Relation: http://purl.org/au-research/grants/arc/DP190100580
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- Description: In this paper, a new nonsmooth optimization-based algorithm for solving large-scale regression problems is introduced. The regression problem is modeled as fully-connected feedforward neural networks with one hidden layer, piecewise linear activation, and the (Formula presented.) -loss functions. A modified version of the limited memory bundle method is applied to minimize this nonsmooth objective. In addition, a novel constructive approach for automated determination of the proper number of hidden nodes is developed. Finally, large real-world data sets are used to evaluate the proposed algorithm and to compare it with some state-of-the-art neural network algorithms for regression. The results demonstrate the superiority of the proposed algorithm as a predictive tool in most data sets used in numerical experiments. © 2023 by the authors.
Ode to form
- Authors: Mestrom, Sanne
- Date: 2012
- Type: Text , Visual art work
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Soil moisture, organic carbon, and nitrogen content prediction with hyperspectral data using regression models
- Authors: Datta, Dristi , Paul, Manoranjan , Murshed, Manzur , Teng, Shyh Wei , Schmidtke, Leigh
- Date: 2022
- Type: Text , Journal article
- Relation: Sensors (Basel, Switzerland) Vol. 22, no. 20 (2022), p.
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- Description: Soil moisture, soil organic carbon, and nitrogen content prediction are considered significant fields of study as they are directly related to plant health and food production. Direct estimation of these soil properties with traditional methods, for example, the oven-drying technique and chemical analysis, is a time and resource-consuming approach and can predict only smaller areas. With the significant development of remote sensing and hyperspectral (HS) imaging technologies, soil moisture, carbon, and nitrogen can be estimated over vast areas. This paper presents a generalized approach to predicting three different essential soil contents using a comprehensive study of various machine learning (ML) models by considering the dimensional reduction in feature spaces. In this study, we have used three popular benchmark HS datasets captured in Germany and Sweden. The efficacy of different ML algorithms is evaluated to predict soil content, and significant improvement is obtained when a specific range of bands is selected. The performance of ML models is further improved by applying principal component analysis (PCA), a dimensional reduction method that works with an unsupervised learning method. The effect of soil temperature on soil moisture prediction is evaluated in this study, and the results show that when the soil temperature is considered with the HS band, the soil moisture prediction accuracy does not improve. However, the combined effect of band selection and feature transformation using PCA significantly enhances the prediction accuracy for soil moisture, carbon, and nitrogen content. This study represents a comprehensive analysis of a wide range of established ML regression models using data preprocessing, effective band selection, and data dimension reduction and attempt to understand which feature combinations provide the best accuracy. The outcomes of several ML models are verified with validation techniques and the best- and worst-case scenarios in terms of soil content are noted. The proposed approach outperforms existing estimation techniques.
Efficient data gathering in 3D linear underwater wireless sensor networks using sink mobility
- Authors: Akbar, Mariam , Javaid, Nadeem , Khan, Ayesha , Imran, Muhammad , Shoaib, Muhammad , Vasilakos, Athanasios
- Date: 2016
- Type: Text , Journal article
- Relation: Sensors (Switzerland) Vol. 16, no. 3 (2016), p.
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- Description: Due to the unpleasant and unpredictable underwater environment, designing an energy-efficient routing protocol for underwater wireless sensor networks (UWSNs) demands more accuracy and extra computations. In the proposed scheme, we introduce a mobile sink (MS), i.e., an autonomous underwater vehicle (AUV), and also courier nodes (CNs), to minimize the energy consumption of nodes. MS and CNs stop at specific stops for data gathering; later on, CNs forward the received data to the MS for further transmission. By the mobility of CNs and MS, the overall energy consumption of nodes is minimized. We perform simulations to investigate the performance of the proposed scheme and compare it to preexisting techniques. Simulation results are compared in terms of network lifetime, throughput, path loss, transmission loss and packet drop ratio. The results show that the proposed technique performs better in terms of network lifetime, throughput, path loss and scalability. © 2016 by the authors; licensee MDPI, Basel, Switzerland.
Conical averagedness and convergence analysis of fixed point algorithms
- Authors: Bartz, Sedi , Dao, Minh , Phan, Hung
- Date: 2022
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 82, no. 2 (2022), p. 351-373
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- Description: We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the stability under relaxations, convex combinations and compositions. We derive conical averagedness properties of resolvents of generalized monotone operators. These properties are then utilized in order to analyze the convergence of the proximal point algorithm, the forward–backward algorithm, and the adaptive Douglas–Rachford algorithm. Our study unifies, improves and casts new light on recent studies of these topics. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Magic and antimagic labeling of graphs
- Authors: Sugeng, Kiki Ariyanti
- Date: 2005
- Type: Text , Thesis , PhD
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- Description: "A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling."
- Description: Doctor of Philosophy
Strongly regular points of mappings
- Authors: Abbasi, Malek , Théra, Michel
- Date: 2021
- Type: Text , Journal article
- Relation: Fixed Point Theory and Algorithms for Sciences and Engineering Vol. 2021, no. 1 (Journal article 2021), p.
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- Description: In this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of a given mapping at a certain point. Then, we discuss the Hoffman estimation and achieve some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows one to calculate the coefficient of the error bound. © 2021, The Author(s).
On graphs with cyclic defect or excess
- Authors: Delorme, Charles , Pineda-Villavicencio, Guillermo
- Date: 2010
- Type: Text , Journal article
- Relation: Electronic Journal of Combinatorics Vol. 17, no. 1 (2010), p.
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- Description: The Moore bound constitutes both an upper bound on the order of a graph of maximum degree d and diameter D = k and a lower bound on the order of a graph of minimum degree d and odd girth g = 2k + 1. Graphs missing or exceeding the Moore bound by ε are called graphs with defect or excess ε, respectively. While Moore graphs (graphs with ε = 0) and graphs with defect or excess 1 have been characterized almost completely, graphs with defect or excess 2 represent a wide unexplored area. Graphs with defect (excess) 2 satisfy the equation Gd,k(A) = Jn +B (Gd,k(A) = Jn - B), where A denotes the adjacency matrix of the graph in question, n its order, Jn the n × n matrix whose entries are all 1's, B the adjacency matrix of a union of vertex-disjoint cycles, and Gd,k(x) a polynomial with integer coefficients such that the matrix Gd,k(A) gives the number of paths of length at most k joining each pair of vertices in the graph. In particular, if B is the adjacency matrix of a cycle of order n we call the corresponding graphs graphs with cyclic defect or excess; these graphs are the subject of our attention in this paper. We prove the non-existence of infinitely many such graphs. As the highlight of the paper we provide the asymptotic upper bound of O(64/3 d3/2) for the number of graphs of odd degree d ≥ 3 and cyclic defect or excess. This bound is in fact quite generous, and as a way of illustration, we show the non-existence of some families of graphs of odd degree d ≥ 3 and cyclic defect or excess. Actually, we conjecture that, apart from the Möbius ladder on 8 vertices, no non-trivial graph of any degree ≥ 3 and cyclic defect or excess exists.
Comparative analysis of machine and deep learning models for soil properties prediction from hyperspectral visual band
- Authors: Datta, Dristi , Paul, Manoranjan , Murshed, Manzur , Teng, Shyh Wei , Schmidtke, Leigh
- Date: 2023
- Type: Text , Journal article
- Relation: Environments Vol. 10, no. 5 (2023), p. 77
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- Description: Estimating various properties of soil, including moisture, carbon, and nitrogen, is crucial for studying their correlation with plant health and food production. However, conventional methods such as oven-drying and chemical analysis are laborious, expensive, and only feasible for a limited land area. With the advent of remote sensing technologies like multi/hyperspectral imaging, it is now possible to predict soil properties non-invasive and cost-effectively for a large expanse of bare land. Recent research shows the possibility of predicting those soil contents from a wide range of hyperspectral data using good prediction algorithms. However, these kinds of hyperspectral sensors are expensive and not widely available. Therefore, this paper investigates different machine and deep learning techniques to predict soil nutrient properties using only the red (R), green (G), and blue (B) bands data to propose a suitable machine/deep learning model that can be used as a rapid soil test. Another objective of this research is to observe and compare the prediction accuracy in three cases i. hyperspectral band ii. full spectrum of the visual band, and iii. three-channel of RGB band and provide a guideline to the user on which spectrum information they should use to predict those soil properties. The outcome of this research helps to develop a mobile application that is easy to use for a quick soil test. This research also explores learning-based algorithms with significant feature combinations and their performance comparisons in predicting soil properties from visual band data. For this, we also explore the impact of dimensional reduction (i.e., principal component analysis) and transformations (i.e., empirical mode decomposition) of features. The results show that the proposed model can comparably predict the soil contents from the three-channel RGB data.
Structural properties and labeling of graphs
- Authors: Dafik
- Date: 2007
- Type: Text , Thesis , PhD
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- Description: The complexity in building massive scale parallel processing systems has re- sulted in a growing interest in the study of interconnection networks design. Network design affects the performance, cost, scalability, and availability of parallel computers. Therefore, discovering a good structure of the network is one of the basic issues. From modeling point of view, the structure of networks can be naturally stud- ied in terms of graph theory. Several common desirable features of networks, such as large number of processing elements, good throughput, short data com- munication delay, modularity, good fault tolerance and diameter vulnerability correspond to properties of the underlying graphs of networks, including large number of vertices, small diameter, high connectivity and overall balance (or regularity) of the graph or digraph. The first part of this thesis deals with the issue of interconnection networks ad- dressing system. From graph theory point of view, this issue is mainly related to a graph labeling. We investigate a special family of graph labeling, namely antimagic labeling of a class of disconnected graphs. We present new results in super (a; d)-edge antimagic total labeling for disjoint union of multiple copies of special families of graphs. The second part of this thesis deals with the issue of regularity of digraphs with the number of vertices close to the upper bound, called the Moore bound, which is unobtainable for most values of out-degree and diameter. Regularity of the underlying graph of a network is often considered to be essential since the flow of messages and exchange of data between processing elements will be on average faster if there is a similar number of interconnections coming in and going out of each processing element. This means that the in-degree and out-degree of each processing element must be the same or almost the same. Our new results show that digraphs of order two less than Moore bound are either diregular or almost diregular.
- Description: Doctor of Philosophy
Linkedness of cartesian products of complete graphs
- 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
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- 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
You Can’t Beat Relating with God for Spiritual Well-Being: Comparing a Generic Version with the Original Spiritual Well-Being Questionnaire Called SHALOM
- Authors: Fisher, John
- Date: 2013
- Type: Text , Journal article
- Relation: Religions Vol. 2013, no. 4 (2013), p. 325-335
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- Description: The Spiritual Health And Life-Orientation Measure (SHALOM) is a 20-item instrument that assesses the quality of relationships of the respondent with self, others, the environment and/or a Transcendent Other. In the Transcendental domain, four of the five items had the words ‘God, ‘Divine’ and ‘Creator’ replaced by the word ‘Transcendent’ to make the survey more generic by removing any implied reference to any god or religion. Invitations to complete a web survey were sent to people who had published papers in spirituality, or belonged to associations for spirituality or religious studies, as well as the Australian Atheist Forum. 409 respondents from 14 geographic regions, completed the survey. Confirmatory factor analysis revealed that the modified, generic form of SHALOM showed acceptable model fit, comprising four clearly delineated domains of spiritual well-being. The paper analyses the results derived from using the modified, generic version and, in comparison with results of applications of the original survey instrument, concludes with discussion of the comparative utility of each of the versions of SHALOM. Further studies with more people are warranted, but, from evidence presented here, it looks like you can’t beat relating with God for spiritual well-being.
New Farkas-type results for vector-valued functions : A non-abstract approach
- Authors: Dinh, Nguyen , Goberna, Miguel , Long, Dang , Lopez-Cerda, Marco
- Date: 2019
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 182, no. 1 (2019), p. 4-29
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- Description: This paper provides new Farkas-type results characterizing the inclusion of a given set, called contained set, into a second given set, called container set, both of them are subsets of some locally convex space, called decision space. The contained and the container sets are described here by means of vector functions from the decision space to other two locally convex spaces which are equipped with the partial ordering associated with given convex cones. These new Farkas lemmas are obtained via the complete characterization of the conic epigraphs of certain conjugate mappings which constitute the core of our approach. In contrast with a previous paper of three of the authors (Dinh et al. in J Optim Theory Appl 173:357-390, 2017), the aimed characterizations of the containment are expressed here in terms of the data.