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28Bagirov, Adil
25Gao, David
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15Wu, Zhiyou
14Rubinov, Alex
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13Roshchina, Vera
13Ugon, Julien
11Outrata, Jiri
9Sukhorukova, Nadezda
7Goberna, Miguel
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1230103 Numerical and Computational Mathematics
390802 Computation Theory and Mathematics
360906 Electrical and Electronic Engineering
220101 Pure Mathematics
20Global optimization
180905 Civil Engineering
18Nonsmooth optimization
160913 Mechanical Engineering
140801 Artificial Intelligence and Image Processing
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8Canonical duality theory
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Solving second-order conic systems with variable precision

- Cucker, Felipe, Peña, Javier, Roshchina, Vera

**Authors:**Cucker, Felipe , Peña, Javier , Roshchina, Vera**Date:**2014**Type:**Text , Journal article**Relation:**Mathematical Programming Vol. 150, no. 2 (2014), p. 217-250**Full Text:**false**Reviewed:****Description:**We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of arithmetic operations and the finest precision required are exhibited. © 2014, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

Some preconditioners for systems of linear inequalities

- Peña, Javier, Roshchina, Vera, Soheili, Negar

**Authors:**Peña, Javier , Roshchina, Vera , Soheili, Negar**Date:**2014**Type:**Text , Journal article**Relation:**Optimization Letters Vol. 8, no. 7 (2014), p. 2145-2152**Full Text:**false**Reviewed:****Description:**We show that a combination of two simple preprocessing steps would generally improve the conditioning of a homogeneous system of linear inequalities. Our approach is based on a comparison among three different but related notions of conditioning for linear inequalities. © 2014, Springer-Verlag Berlin Heidelberg.

Special Issue on recent advances in continuous optimization on the occasion of the 25th European conference on Operational Research (EURO XXV 2012)

- Weber, Gerhard-Wilhelm, Kruger, Alexander, Martinez-Legaz, Juan, Mordukhovich, Boris, Sakalauskas, Leonidas

**Authors:**Weber, Gerhard-Wilhelm , Kruger, Alexander , Martinez-Legaz, Juan , Mordukhovich, Boris , Sakalauskas, Leonidas**Date:**2014**Type:**Text , Journal article**Relation:**Optimization Vol. 63, no. 1 (2014), p. 1-5**Full Text:****Reviewed:**

**Authors:**Weber, Gerhard-Wilhelm , Kruger, Alexander , Martinez-Legaz, Juan , Mordukhovich, Boris , Sakalauskas, Leonidas**Date:**2014**Type:**Text , Journal article**Relation:**Optimization Vol. 63, no. 1 (2014), p. 1-5**Full Text:****Reviewed:**

Spline regression models for complex multi-modal regulatory networks

- Ozmen, Ayse, Kropat, Erik, Weber, Gerhard-Wilhelm

**Authors:**Ozmen, Ayse , Kropat, Erik , Weber, Gerhard-Wilhelm**Date:**2014**Type:**Text , Journal article**Relation:**Optimization Methods and Software Vol. 29, no. 3 (2014), p. 515-534**Full Text:**false**Reviewed:****Description:**Complex regulatory networks often have to be further expanded and improved with regard to the unknown effects of additional parameters and factors that can emit a disturbing influence on the key variables under consideration. The concept of target-environment (TE) networks provides a holistic framework for the analysis of such parameter-dependent multi-modal systems. In this study, we consider time-discrete TE regulatory systems with spline entries. We introduce a new regression model for these particular two-modal systems that allows us to determine the unknown system parameters by applying the multivariate adaptive regression spline (MARS) technique and the newly developed conic multivariate adaptive regression spline (CMARS) method. We obtain a relaxation by means of continuous optimization, especially, conic quadratic programming (CQP) that could be conducted by interior point methods. Finally, a numerical example demonstrates the efficiency of the spline-based approach.

Structure learning of Bayesian Networks using global optimization with applications in data classification

- Taheri, Sona, Mammadov, Musa

**Authors:**Taheri, Sona , Mammadov, Musa**Date:**2014**Type:**Text , Journal article**Relation:**Optimization Letters Vol. 9, no. 5 (2014), p. 931-948**Full Text:****Reviewed:****Description:**Bayesian Networks are increasingly popular methods of modeling uncertainty in artificial intelligence and machine learning. A Bayesian Network consists of a directed acyclic graph in which each node represents a variable and each arc represents probabilistic dependency between two variables. Constructing a Bayesian Network from data is a learning process that consists of two steps: learning structure and learning parameter. Learning a network structure from data is the most difficult task in this process. This paper presents a new algorithm for constructing an optimal structure for Bayesian Networks based on optimization. The algorithm has two major parts. First, we define an optimization model to find the better network graphs. Then, we apply an optimization approach for removing possible cycles from the directed graphs obtained in the first part which is the first of its kind in the literature. The main advantage of the proposed method is that the maximal number of parents for variables is not fixed a priory and it is defined during the optimization procedure. It also considers all networks including cyclic ones and then choose a best structure by applying a global optimization method. To show the efficiency of the algorithm, several closely related algorithms including unrestricted dependency Bayesian Network algorithm, as well as, benchmarks algorithms SVM and C4.5 are employed for comparison. We apply these algorithms on data classification; data sets are taken from the UCI machine learning repository and the LIBSVM. © 2014, Springer-Verlag Berlin Heidelberg.

**Authors:**Taheri, Sona , Mammadov, Musa**Date:**2014**Type:**Text , Journal article**Relation:**Optimization Letters Vol. 9, no. 5 (2014), p. 931-948**Full Text:****Reviewed:****Description:**Bayesian Networks are increasingly popular methods of modeling uncertainty in artificial intelligence and machine learning. A Bayesian Network consists of a directed acyclic graph in which each node represents a variable and each arc represents probabilistic dependency between two variables. Constructing a Bayesian Network from data is a learning process that consists of two steps: learning structure and learning parameter. Learning a network structure from data is the most difficult task in this process. This paper presents a new algorithm for constructing an optimal structure for Bayesian Networks based on optimization. The algorithm has two major parts. First, we define an optimization model to find the better network graphs. Then, we apply an optimization approach for removing possible cycles from the directed graphs obtained in the first part which is the first of its kind in the literature. The main advantage of the proposed method is that the maximal number of parents for variables is not fixed a priory and it is defined during the optimization procedure. It also considers all networks including cyclic ones and then choose a best structure by applying a global optimization method. To show the efficiency of the algorithm, several closely related algorithms including unrestricted dependency Bayesian Network algorithm, as well as, benchmarks algorithms SVM and C4.5 are employed for comparison. We apply these algorithms on data classification; data sets are taken from the UCI machine learning repository and the LIBSVM. © 2014, Springer-Verlag Berlin Heidelberg.

Turnpike theorem for an infinite horizon optimal control problem with time delay

**Authors:**Mammadov, Musa**Date:**2014**Type:**Text , Journal article**Relation:**SIAM Journal on Control and Optimization Vol. 52, no. 1 (2014), p. 420-438**Full Text:****Reviewed:****Description:**An optimal control problem for systems described by a special class of nonlinear differential equations with time delay is considered. The cost functional adopted could be considered as an analogue of the terminal functional defined over an infinite time horizon. The existence of optimal solutions as well as the asymptotic stability of optimal trajectories (that is, the turnpike property) are established under some quite mild restrictions on the nonlinearities of the functions involved in the description of the problem. Such mild restrictions on the nonlinearities allowed us to apply these results to a blood cell production model. Â© 2014 Society for Industrial and Applied Mathematics.

**Authors:**Mammadov, Musa**Date:**2014**Type:**Text , Journal article**Relation:**SIAM Journal on Control and Optimization Vol. 52, no. 1 (2014), p. 420-438**Full Text:****Reviewed:****Description:**An optimal control problem for systems described by a special class of nonlinear differential equations with time delay is considered. The cost functional adopted could be considered as an analogue of the terminal functional defined over an infinite time horizon. The existence of optimal solutions as well as the asymptotic stability of optimal trajectories (that is, the turnpike property) are established under some quite mild restrictions on the nonlinearities of the functions involved in the description of the problem. Such mild restrictions on the nonlinearities allowed us to apply these results to a blood cell production model. Â© 2014 Society for Industrial and Applied Mathematics.

- Jelinek, Herbert, Kelarev, Andrei, Robinson, Dean, Stranieri, Andrew, Cornforth, David

**Authors:**Jelinek, Herbert , Kelarev, Andrei , Robinson, Dean , Stranieri, Andrew , Cornforth, David**Date:**2014**Type:**Text , Journal article**Relation:**Applied Soft Computing Vol. 14, no. PART A (2014), p. 81-87**Full Text:**false**Reviewed:****Description:**This work investigates the effectiveness of using computer-based machine learning regression algorithms and meta-regression methods to predict performance data for Australian football players based on parameters collected during daily physiological tests. Three experiments are described. The first uses all available data with a variety of regression techniques. The second uses a subset of features selected from the available data using the Random Forest method. The third used meta-regression with the selected feature subset. Our experiments demonstrate that feature selection and meta-regression methods improve the accuracy of predictions for match performance of Australian football players based on daily data of medical tests, compared to regression methods alone. Meta-regression methods and feature selection were able to obtain performance prediction outcomes with significant correlation coefficients. The best results were obtained by the additive regression based on isotonic regression for a set of most influential features selected by Random Forest. This model was able to predict athlete performance data with a correlation coefficient of 0.86 (p < 0.05). Â© 2013 Published by Elsevier B.V. All rights reserved.**Description:**C1

A new auxiliary function method for general constrained global optimization

- Wu, Zhiyou, Bai, Fusheng, Yang, Yongjian, Mammadov, Musa

**Authors:**Wu, Zhiyou , Bai, Fusheng , Yang, Yongjian , Mammadov, Musa**Date:**2013**Type:**Text , Journal article**Relation:**Optimization Vol. 62, no. 2 (2013), p. 193-210**Full Text:****Reviewed:****Description:**In this article, we first propose a method to obtain an approximate feasible point for general constrained global optimization problems (with both inequality and equality constraints). Then we propose an auxiliary function method to obtain a global minimizer or an approximate global minimizer with a required precision for general global optimization problems by locally solving some unconstrained programming problems. Some numerical examples are reported to demonstrate the efficiency of the present optimization method. © 2013 Taylor & Francis.**Description:**2003011103

**Authors:**Wu, Zhiyou , Bai, Fusheng , Yang, Yongjian , Mammadov, Musa**Date:**2013**Type:**Text , Journal article**Relation:**Optimization Vol. 62, no. 2 (2013), p. 193-210**Full Text:****Reviewed:****Description:**In this article, we first propose a method to obtain an approximate feasible point for general constrained global optimization problems (with both inequality and equality constraints). Then we propose an auxiliary function method to obtain a global minimizer or an approximate global minimizer with a required precision for general global optimization problems by locally solving some unconstrained programming problems. Some numerical examples are reported to demonstrate the efficiency of the present optimization method. © 2013 Taylor & Francis.**Description:**2003011103

- Bagirov, Adil, Barton, Andrew, Mala-Jetmarova, Helena, Al Nuaimat, Alia, Ahmed, S. T., Sultanova, Nargiz, Yearwood, John

**Authors:**Bagirov, Adil , Barton, Andrew , Mala-Jetmarova, Helena , Al Nuaimat, Alia , Ahmed, S. T. , Sultanova, Nargiz , Yearwood, John**Date:**2013**Type:**Text , Journal article**Relation:**Mathematical and Computer Modelling Vol. 57, no. 3-4 (2013), p. 873-886**Relation:**http://purl.org/au-research/grants/arc/LP0990908**Full Text:**false**Reviewed:****Description:**The operation of a water distribution system is a complex task which involves scheduling of pumps, regulating water levels of storages, and providing satisfactory water quality to customers at required flow and pressure. Pump scheduling is one of the most important tasks of the operation of a water distribution system as it represents the major part of its operating costs. In this paper, a novel approach for modeling of explicit pump scheduling to minimize energy consumption by pumps is introduced which uses the pump start/end run times as continuous variables, and binary integer variables to describe the pump status at the beginning of the scheduling period. This is different from other approaches where binary integer variables for each hour are typically used, which is considered very impractical from an operational perspective. The problem is formulated as a mixed integer nonlinear programming problem, and a new algorithm is developed for its solution. This algorithm is based on the combination of the grid search with the Hooke-Jeeves pattern search method. The performance of the algorithm is evaluated using literature test problems applying the hydraulic simulation model EPANet. © 2012 Elsevier Ltd.**Description:**2003010583

Complete solutions and triality theory to a nonconvex optimization problem with double-well potential in Rn

- Morales-Silva, Daniel, Gao, David

**Authors:**Morales-Silva, Daniel , Gao, David**Date:**2013**Type:**Text , Journal article**Relation:**Numerical Algebra, Control and Optimization Vol. 3, no. 2 (2013), p. 271-282**Full Text:****Reviewed:****Description:**The main purpose of this research note is to show that the triality theory can always be used to identify both global minimizer and the biggest local maximizer in global optimization. An open problem left on the double- min duality is solved for a nonconvex optimization problem with double-well potential in ℝn, which leads to a complete set of analytical solutions. Also a convergency theorem is proved for linear perturbation canonical dual method, which can be used for solving global optimization problems with multiple so- lutions. The methods and results presented in this note pave the way towards the proof of the triality theory in general cases.

**Authors:**Morales-Silva, Daniel , Gao, David**Date:**2013**Type:**Text , Journal article**Relation:**Numerical Algebra, Control and Optimization Vol. 3, no. 2 (2013), p. 271-282**Full Text:****Reviewed:****Description:**The main purpose of this research note is to show that the triality theory can always be used to identify both global minimizer and the biggest local maximizer in global optimization. An open problem left on the double- min duality is solved for a nonconvex optimization problem with double-well potential in ℝn, which leads to a complete set of analytical solutions. Also a convergency theorem is proved for linear perturbation canonical dual method, which can be used for solving global optimization problems with multiple so- lutions. The methods and results presented in this note pave the way towards the proof of the triality theory in general cases.

Euler-Goursat-like formula via Laplace-Borel duality

- Gurarii, V. P., Gillam, David

**Authors:**Gurarii, V. P. , Gillam, David**Date:**2013**Type:**Text , Journal article**Relation:**Journal of Mathematical Analysis and Applications Vol. 408, no. 2 (2013), p. 655-668**Full Text:****Reviewed:****Description:**The Goursat formula for the hypergeometric function extends the Euler-Gauss relation to the case of logarithmic singularities. We study the monodromic functional equation associated with a perturbation of the Bessel differential equation by means of a variant of the Laplace-Borel technique: we introduce and study a related monodromic equation in the dual complex plane. This construction is a crucial element in our proof of a duality theorem that leads to an extension of the Euler-Gauss-Goursat formula for hypergeometric functions to a substantially larger class of functions. © 2013 Elsevier Ltd.**Description:**C1

**Authors:**Gurarii, V. P. , Gillam, David**Date:**2013**Type:**Text , Journal article**Relation:**Journal of Mathematical Analysis and Applications Vol. 408, no. 2 (2013), p. 655-668**Full Text:****Reviewed:****Description:**The Goursat formula for the hypergeometric function extends the Euler-Gauss relation to the case of logarithmic singularities. We study the monodromic functional equation associated with a perturbation of the Bessel differential equation by means of a variant of the Laplace-Borel technique: we introduce and study a related monodromic equation in the dual complex plane. This construction is a crucial element in our proof of a duality theorem that leads to an extension of the Euler-Gauss-Goursat formula for hypergeometric functions to a substantially larger class of functions. © 2013 Elsevier Ltd.**Description:**C1

Extraction and processing of real time strain of embedded FBG sensors using a fixed filter FBG circuit and an artificial neural network

- Kahandawa, Gayan, Epaarachchi, Jayantha, Wang, Hao, Canning, John, Lau, Alan

**Authors:**Kahandawa, Gayan , Epaarachchi, Jayantha , Wang, Hao , Canning, John , Lau, Alan**Date:**2013**Type:**Text , Journal article**Relation:**Measurement: Journal of the International Measurement Confederation Vol. 46, no. 10 (2013), p. 4045-4051**Full Text:****Reviewed:****Description:**Fibre Bragg Grating (FBG) sensors have been used in the development of structural health monitoring (SHM) and damage detection systems for advanced composite structures over several decades. Unfortunately, to date only a handful of appropriate configurations and algorithm sare available for using in SHM systems have been developed. This paper reveals a novel configuration of FBG sensors to acquire strain reading and an integrated statistical approach to analyse data in real time. The proposed configuration has proven its capability to overcome practical constraints and the engineering challenges associated with FBG-based SHM systems. A fixed filter decoding system and an integrated artificial neural network algorithm for extracting strain from embedded FBG sensor were proposed and experimentally proved. Furthermore, the laboratory level experimental data was used to verify the accuracy of the system and it was found that the error levels were less than 0.3% in predictions. The developed SMH system using this technology has been submitted to US patent office and will be available for use of aerospace applications in due course. © 2013 Elsevier Ltd. All rights reserved.

**Authors:**Kahandawa, Gayan , Epaarachchi, Jayantha , Wang, Hao , Canning, John , Lau, Alan**Date:**2013**Type:**Text , Journal article**Relation:**Measurement: Journal of the International Measurement Confederation Vol. 46, no. 10 (2013), p. 4045-4051**Full Text:****Reviewed:****Description:**Fibre Bragg Grating (FBG) sensors have been used in the development of structural health monitoring (SHM) and damage detection systems for advanced composite structures over several decades. Unfortunately, to date only a handful of appropriate configurations and algorithm sare available for using in SHM systems have been developed. This paper reveals a novel configuration of FBG sensors to acquire strain reading and an integrated statistical approach to analyse data in real time. The proposed configuration has proven its capability to overcome practical constraints and the engineering challenges associated with FBG-based SHM systems. A fixed filter decoding system and an integrated artificial neural network algorithm for extracting strain from embedded FBG sensor were proposed and experimentally proved. Furthermore, the laboratory level experimental data was used to verify the accuracy of the system and it was found that the error levels were less than 0.3% in predictions. The developed SMH system using this technology has been submitted to US patent office and will be available for use of aerospace applications in due course. © 2013 Elsevier Ltd. All rights reserved.

Finite element computations over quadtree meshes : Strain smoothing and semi-analytical formulation

- Natarajan, Sundararajan, Ooi, Ean Tat, Song, Chongmin

**Authors:**Natarajan, Sundararajan , Ooi, Ean Tat , Song, Chongmin**Date:**2013**Type:**Text , Journal article**Relation:**International Journal of Advances in Engineering Sciences and Applied Mathematics Vol. 7, no. 3 (2013), p. 124-133**Full Text:****Reviewed:****Description:**In this paper, we discuss two alternate techniques to treat hanging nodes in a quadtree mesh. Both the techniques share similarities, in that, they require only boundary information. Moreover, they do not require an explicit form of the shape functions, unlike the conventional approaches, for example, as in the work of Gupta (Int J Numer Methods Eng 12:35, 1978) or Tabarraei and Sukumar (Finite Elem Anal Des 41:686, 2005). Hence, no special numerical integration technique is required. One of the techniques relies on the strain projection procedure, whilst the other is based on the scaled boundary finite element method. Numerical examples are presented to demonstrate the accuracy and the convergence properties of the two techniques.

**Authors:**Natarajan, Sundararajan , Ooi, Ean Tat , Song, Chongmin**Date:**2013**Type:**Text , Journal article**Relation:**International Journal of Advances in Engineering Sciences and Applied Mathematics Vol. 7, no. 3 (2013), p. 124-133**Full Text:****Reviewed:****Description:**In this paper, we discuss two alternate techniques to treat hanging nodes in a quadtree mesh. Both the techniques share similarities, in that, they require only boundary information. Moreover, they do not require an explicit form of the shape functions, unlike the conventional approaches, for example, as in the work of Gupta (Int J Numer Methods Eng 12:35, 1978) or Tabarraei and Sukumar (Finite Elem Anal Des 41:686, 2005). Hence, no special numerical integration technique is required. One of the techniques relies on the strain projection procedure, whilst the other is based on the scaled boundary finite element method. Numerical examples are presented to demonstrate the accuracy and the convergence properties of the two techniques.

Fractal bodies invisible in 2 and 3 directions

- Plakhov, Alexander, Roshchina, Vera

**Authors:**Plakhov, Alexander , Roshchina, Vera**Date:**2013**Type:**Text , Journal article**Relation:**Discrete and Continuous Dynamical Systems - Series A Vol. 33, no. 4 (2013), p. 1615-1631**Full Text:****Reviewed:****Description:**We study the problem of invisibility for bodies with a mirror surface in the framework of geometrical optics. We show that for any two given directions it is possible to construct a two-dimensional fractal body invisible in these directions. Moreover, there exists a three-dimensional fractal body invisible in three orthogonal directions. The work continues the previous study in [1, 12], where two-dimensional bodies invisible in one direction and threedimensional bodies invisible in one and two orthogonal directions were constructed.**Description:**2003010679

**Authors:**Plakhov, Alexander , Roshchina, Vera**Date:**2013**Type:**Text , Journal article**Relation:**Discrete and Continuous Dynamical Systems - Series A Vol. 33, no. 4 (2013), p. 1615-1631**Full Text:****Reviewed:****Description:**We study the problem of invisibility for bodies with a mirror surface in the framework of geometrical optics. We show that for any two given directions it is possible to construct a two-dimensional fractal body invisible in these directions. Moreover, there exists a three-dimensional fractal body invisible in three orthogonal directions. The work continues the previous study in [1, 12], where two-dimensional bodies invisible in one direction and threedimensional bodies invisible in one and two orthogonal directions were constructed.**Description:**2003010679

Globally convergent algorithms for solving unconstrained optimization problems

- Taheri, Sona, Mammadov, Musa, Seifollahi, Sattar

**Authors:**Taheri, Sona , Mammadov, Musa , Seifollahi, Sattar**Date:**2013**Type:**Text , Journal article**Relation:**Optimization Vol. , no. (2013), p. 1-15**Full Text:****Reviewed:****Description:**New algorithms for solving unconstrained optimization problems are presented based on the idea of combining two types of descent directions: the direction of anti-gradient and either the Newton or quasi-Newton directions. The use of latter directions allows one to improve the convergence rate. Global and superlinear convergence properties of these algorithms are established. Numerical experiments using some unconstrained test problems are reported. Also, the proposed algorithms are compared with some existing similar methods using results of experiments. This comparison demonstrates the efficiency of the proposed combined methods.

**Authors:**Taheri, Sona , Mammadov, Musa , Seifollahi, Sattar**Date:**2013**Type:**Text , Journal article**Relation:**Optimization Vol. , no. (2013), p. 1-15**Full Text:****Reviewed:****Description:**New algorithms for solving unconstrained optimization problems are presented based on the idea of combining two types of descent directions: the direction of anti-gradient and either the Newton or quasi-Newton directions. The use of latter directions allows one to improve the convergence rate. Global and superlinear convergence properties of these algorithms are established. Numerical experiments using some unconstrained test problems are reported. Also, the proposed algorithms are compared with some existing similar methods using results of experiments. This comparison demonstrates the efficiency of the proposed combined methods.

Hyperbolic smoothing function method for minimax problems

- Bagirov, Adil, Al Nuaimat, Alia, Sultanova, Nargiz

**Authors:**Bagirov, Adil , Al Nuaimat, Alia , Sultanova, Nargiz**Date:**2013**Type:**Text , Journal article**Relation:**Optimization Vol. 62, no. 6 (2013), p. 759-782**Full Text:**false**Reviewed:****Description:**In this article, an approach for solving finite minimax problems is proposed. This approach is based on the use of hyperbolic smoothing functions. In order to apply the hyperbolic smoothing we reformulate the objective function in the minimax problem and study the relationship between the original minimax and reformulated problems. We also study main properties of the hyperbolic smoothing function. Based on these results an algorithm for solving the finite minimax problem is proposed and this algorithm is implemented in general algebraic modelling system. We present preliminary results of numerical experiments with well-known nonsmooth optimization test problems. We also compare the proposed algorithm with the algorithm that uses the exponential smoothing function as well as with the algorithm based on nonlinear programming reformulation of the finite minimax problem. © 2013 Copyright Taylor and Francis Group, LLC.**Description:**2003011099

On large bipartite graphs of diameter 3

- Feria-Purón, Ramiro, Miller, Mirka, Pineda-Villavicencio, Guillermo

**Authors:**Feria-Purón, Ramiro , Miller, Mirka , Pineda-Villavicencio, Guillermo**Date:**2013**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 313, no. 4 (2013), p. 381-390**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**We consider the bipartite version of the degree/diameter problem, namely, given natural numbers dâ‰¥2 and Dâ‰¥2, find the maximum number N b(d,D) of vertices in a bipartite graph of maximum degree d and diameter D. In this context, the bipartite Moore bound Mb(d,D) represents a general upper bound for Nb(d,D). Bipartite graphs of order Mb(d,D) are very rare, and determining Nb(d,D) still remains an open problem for most (d,D) pairs. This paper is a follow-up of our earlier paper (Feria-PurÃ³n and Pineda-Villavicencio, 2012 [5]), where a study on bipartite (d,D,-4)-graphs (that is, bipartite graphs of order M b(d,D)-4) was carried out. Here we first present some structural properties of bipartite (d,3,-4)-graphs, and later prove that there are no bipartite (7,3,-4)-graphs. This result implies that the known bipartite (7,3,-6)-graph is optimal, and therefore Nb(7,3)=80. We dub this graph the Hafner-Loz graph after its first discoverers Paul Hafner and Eyal Loz. The approach here presented also provides a proof of the uniqueness of the known bipartite (5,3,-4)-graph, and the non-existence of bipartite (6,3,-4)-graphs. In addition, we discover at least one new largest known bipartite-and also vertex-transitive-graph of degree 11, diameter 3 and order 190, a result which improves by four vertices the previous lower bound for Nb(11,3). © 2012 Elsevier B.V. All rights reserved.**Description:**2003011037

**Authors:**Feria-Purón, Ramiro , Miller, Mirka , Pineda-Villavicencio, Guillermo**Date:**2013**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 313, no. 4 (2013), p. 381-390**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**We consider the bipartite version of the degree/diameter problem, namely, given natural numbers dâ‰¥2 and Dâ‰¥2, find the maximum number N b(d,D) of vertices in a bipartite graph of maximum degree d and diameter D. In this context, the bipartite Moore bound Mb(d,D) represents a general upper bound for Nb(d,D). Bipartite graphs of order Mb(d,D) are very rare, and determining Nb(d,D) still remains an open problem for most (d,D) pairs. This paper is a follow-up of our earlier paper (Feria-PurÃ³n and Pineda-Villavicencio, 2012 [5]), where a study on bipartite (d,D,-4)-graphs (that is, bipartite graphs of order M b(d,D)-4) was carried out. Here we first present some structural properties of bipartite (d,3,-4)-graphs, and later prove that there are no bipartite (7,3,-4)-graphs. This result implies that the known bipartite (7,3,-6)-graph is optimal, and therefore Nb(7,3)=80. We dub this graph the Hafner-Loz graph after its first discoverers Paul Hafner and Eyal Loz. The approach here presented also provides a proof of the uniqueness of the known bipartite (5,3,-4)-graph, and the non-existence of bipartite (6,3,-4)-graphs. In addition, we discover at least one new largest known bipartite-and also vertex-transitive-graph of degree 11, diameter 3 and order 190, a result which improves by four vertices the previous lower bound for Nb(11,3). © 2012 Elsevier B.V. All rights reserved.**Description:**2003011037

Preface: Special issue of JOGO MEC EurOPT 2010-Izmir

- Kasimbeyli, Refail, Mammadov, Musa, Dincer, Cemali

**Authors:**Kasimbeyli, Refail , Mammadov, Musa , Dincer, Cemali**Date:**2013**Type:**Text , Journal article**Relation:**Journal of Global Optimization Vol. 56, no. 2 (June 2013), p. 217-218**Full Text:**false**Reviewed:****Description:**C1

Reachability and controllability of linear switched impulsive systems

- Liu, Chao, Han, Qi, Li, Chuandong, Zhang, Qun

**Authors:**Liu, Chao , Han, Qi , Li, Chuandong , Zhang, Qun**Date:**2013**Type:**Text , Journal article**Relation:**IET Control Theory and Applications Vol. 7, no. 9 (2013), p. 1294-1299**Full Text:**false**Reviewed:****Description:**This study investigates the reachability and controllability of linear switched impulsive systems in which impulsive component is independent of switching among different subsystems. Some crucial geometrical criteria are established. The authors present the fact that the reachable sets and the controllable sets may not be subspaces, if impulsive matrices are singular. While impulsive matrices are reversible, the reachable and controllable subspaces can be determined by two proposed subspace algorithms. The authors also point out that the reachable or controllable subspace is an invariant subspace of the considered systems. Finally, two simple corresponding examples are discussed to illustrate the correctness and effectiveness of the proposed theoretical results. © The Institution of Engineering and Technology 2013.**Description:**C1

- Gao, David, Watson, Layne, Easterling, David, Thacker, William, Billups, Stephen

**Authors:**Gao, David , Watson, Layne , Easterling, David , Thacker, William , Billups, Stephen**Date:**2013**Type:**Text , Journal article**Relation:**Optimization Methods and Software Vol. 28, no. 2 (2013), p. 313-326**Full Text:**false**Reviewed:****Description:**This paper presents a massively parallel global deterministic direct search method (VTDIRECT) for solving nonconvex quadratic minimization problems with either box or1 integer constraints. Using the canonical dual transformation, these well-known NP-hard problems can be reformulated as perfect dual stationary problems (with zero duality gap). Under certain conditions, these dual problems are equivalent to smooth concave maximization over a convex feasible space. Based on a perturbation method proposed by Gao, the integer programming problem is shown to be equivalent to a continuous unconstrained Lipschitzian global optimization problem. The parallel algorithm VTDIRECT is then applied to solve these dual problems to obtain global minimizers. Parallel performance results for several nonconvex quadratic integer programming problems are reported. © 2013 Copyright Taylor and Francis Group, LLC.**Description:**2003010580

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