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28Bagirov, Adil
25Gao, David
23Kruger, Alexander
18López, Marco
15Wu, Zhiyou
14Rubinov, Alex
13Gunawan, Indra
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13Roshchina, Vera
13Ugon, Julien
11Outrata, Jiri
9Sukhorukova, Nadezda
7Goberna, Miguel
6Bai, Fusheng
6Ooi, Ean Tat
6Yearwood, John
5Dinh, Nguyen
5Khandelwal, Manoj
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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
12Subdifferential
11Nonconvex optimization
101202 Building
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8Canonical duality theory
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On optimal control of a sweeping process coupled with an ordinary differential equation

**Authors:**Adam, Lukas , Outrata, Jiri**Date:**2014**Type:**Text , Journal article**Relation:**Discrete and Continuous Dynamical Systems - Series B Vol. 19, no. 9 (November 2014 2014), p. 2709-2738**Full Text:**false**Reviewed:****Description:**We study a special case of an optimal control problem governed by a differential equation and a differential rate{independent variational inequality, both with given initial conditions. Under certain conditions, the variational inequality can be reformulated as a differential inclusion with discontinuous right-hand side. This inclusion is known as sweeping process. We perform a discretization scheme and prove the convergence of optimal solutions of the discretized problems to the optimal solution of the original problem. For the discretized problems we study the properties of the solution map and compute its coderivative. Employing an appropriate chain rule, this enables us to compute the subdifferential of the objective function and to apply a suitable optimization technique to solve the discretized problems. The investigated problem is used to model a situation arising in the area of queuing theory.

**Authors:**Adilov, G. , Rubinov, Alex**Date:**2006**Type:**Text , Journal article**Relation:**Numerical Functional Analysis and Optimization Vol. 27, no. 3-4 (Apr-May 2006), p. 237-257**Full Text:**false**Reviewed:****Description:**A subset B of R-+(n) is B-convex if for all x, y is an element of B and all t is an element of [0, 1] one has max (tx, y) is an element of B. These sets were first investigated in [1, 2]. In this paper, we examine radiant B-convex sets and also introduce and study B-convex functions.**Description:**C1**Description:**2003001836

- Adly, Samir, Hantoute, Abderrahim, Thera, Michel

**Authors:**Adly, Samir , Hantoute, Abderrahim , Thera, Michel**Date:**2016**Type:**Text , Journal article**Relation:**Mathematical Programming Vol. 157, no. 2 (2016), p. 349-374**Full Text:**false**Reviewed:****Description:**The general theory of Lyapunov stability of first-order differential inclusions in Hilbert spaces has been studied by the authors in the previous paper (Adly et al. in Nonlinear Anal 75(3): 985–1008, 2012). This new contribution focuses on the case when the interior of the domain of the maximally monotone operator governing the given differential inclusion is nonempty; this includes in a natural way the finite-dimensional case. The current setting leads to simplified, more explicit criteria and permits some flexibility in the choice of the generalized subdifferentials. Some consequences of the viability of closed sets are given. Our analysis makes use of standard tools from convex and variational analysis. © 2015, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions

- Adly, Samir, Hantoute, Abderrahim, Théra, Michel

**Authors:**Adly, Samir , Hantoute, Abderrahim , Théra, Michel**Date:**2012**Type:**Text , Journal article**Relation:**Nonlinear Analysis: Theory, Methods & Applications Vol. 75, no. 3 (February, 2012), p. 985-1008**Full Text:**false**Reviewed:****Description:**The main objective of this paper is to provide new explicit criteria to characterize weak lower semicontinuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by means of the proximal and basic subdifferentials of the nominal functions while primal conditions are described in terms of the contingent directional derivative. We also propose a unifying review of many other criteria given in the literature. Our approach is based on advanced tools of variational analysis and generalized differentiation.

On SPD method for solving canonical dual problem in post buckling of large deformed elastic beam

**Authors:**Ali, Elaf , Gao, David**Date:**2018**Type:**Text , Journal article**Relation:**Communications in Mathematical Sciences Vol. 16, no. 5 (2018), p. 1225-1240**Full Text:****Reviewed:****Description:**This paper presents a new methodology and algorithm for solving post buckling problems of a large deformed elastic beam. The total potential energy of this beam is a nonconvex functional, which can be used to model both pre- and post-buckling phenomena. By using a canonical dual finite element method, a new primal-dual semi-definite programming (PD-SDP) algorithm is presented, which can be used to obtain all possible post-buckled solutions. Applications are illustrated by several numerical examples with different boundary conditions. We find that the global minimum solution of the nonconvex potential leads to a stable configuration of the buckled beam, the local maximum solution leads to the unbuckled state, and both of these two solutions are numerically stable. However, the local minimum solution leads to an unstable buckled state, which is very sensitive to axial compressive forces, thickness of beam, numerical precision, and the size of finite elements. The method and algorithm proposed in this paper can be used for solving general nonconvex variational problems in engineering and sciences.

**Authors:**Ali, Elaf , Gao, David**Date:**2018**Type:**Text , Journal article**Relation:**Communications in Mathematical Sciences Vol. 16, no. 5 (2018), p. 1225-1240**Full Text:****Reviewed:****Description:**This paper presents a new methodology and algorithm for solving post buckling problems of a large deformed elastic beam. The total potential energy of this beam is a nonconvex functional, which can be used to model both pre- and post-buckling phenomena. By using a canonical dual finite element method, a new primal-dual semi-definite programming (PD-SDP) algorithm is presented, which can be used to obtain all possible post-buckled solutions. Applications are illustrated by several numerical examples with different boundary conditions. We find that the global minimum solution of the nonconvex potential leads to a stable configuration of the buckled beam, the local maximum solution leads to the unbuckled state, and both of these two solutions are numerically stable. However, the local minimum solution leads to an unstable buckled state, which is very sensitive to axial compressive forces, thickness of beam, numerical precision, and the size of finite elements. The method and algorithm proposed in this paper can be used for solving general nonconvex variational problems in engineering and sciences.

Marginal longitudinal semiparametric regression via penalized splines

- Ali-Alkadiri, Mohammad, Carroll, R.J., Wand, M.P.

**Authors:**Ali-Alkadiri, Mohammad , Carroll, R.J. , Wand, M.P.**Date:**2011**Type:**Text , Journal article**Relation:**Statistics and Probablitity Letters Vol. 80, no. 15-16 (2011), p. 1242-1252**Full Text:**false**Reviewed:****Description:**We study the marginal longitudinal nonparametric regression problem and some of its semiparametric extensions. We point out that, while several elaborate proposals for efficient estimation have been proposed, a relative simple and straightforward one, based on penalized splines, has not. After describing our approach, we then explain how Gibbs sampling and the BUGS software can be used to achieve quick and effective implementation. Illustrations are provided for nonparametric regression and additive models.

On Hölder calmness of solution mappings in parametric equilibrium problems

- Anh, Lam Quoc, Kruger, Alexander, Thao, Nguyen

**Authors:**Anh, Lam Quoc , Kruger, Alexander , Thao, Nguyen**Date:**2012**Type:**Text , Journal article**Relation:**TOP Vol. 22, no. 1 (2012), p. 331-342**Full Text:****Reviewed:****Description:**We consider parametric equilibrium problems in metric spaces. Sufficient conditions for the Hölder calmness of solutions are established. We also study the Hölder well-posedness for equilibrium problems in metric spaces.

**Authors:**Anh, Lam Quoc , Kruger, Alexander , Thao, Nguyen**Date:**2012**Type:**Text , Journal article**Relation:**TOP Vol. 22, no. 1 (2012), p. 331-342**Full Text:****Reviewed:****Description:**We consider parametric equilibrium problems in metric spaces. Sufficient conditions for the Hölder calmness of solutions are established. We also study the Hölder well-posedness for equilibrium problems in metric spaces.

On Holder continuity of solution maps of parametric primal and dual Ky Fan inequalities

- Anh, Lam Quoc, Khanh, Phan Quoc, Tam, T. N.

**Authors:**Anh, Lam Quoc , Khanh, Phan Quoc , Tam, T. N.**Date:**2015**Type:**Text , Journal article**Relation:**Top Vol. 23, no. 1 (2015), p. 151-167**Full Text:**false**Reviewed:****Description:**We consider parametric primal and dual Ky Fan inequalities in metric linear spaces. Sufficient conditions for Holder continuity of solutions are established. Many examples are provided to illustrate the essentialness of the imposed assumptions and advantages of the results over existing ones. As applications, we derive this Holder continuity of solutions for constrained minimization and variational inequalities.

Comparative study of RPSALG algorithm for convex semi-infinite programming

- Auslender, Alfred, Ferrer, Albert, Goberna, Miguel, López, Marco

**Authors:**Auslender, Alfred , Ferrer, Albert , Goberna, Miguel , López, Marco**Date:**2014**Type:**Text , Journal article**Relation:**Computational Optimization and Applications Vol. 60, no. 1 (2014), p. 59-87**Full Text:**false**Reviewed:****Description:**The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving min-max convex semi-infinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semi-infinite programming problems. Each iteration of RPSALG involves two types of auxiliary optimization problems: the first one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a non-convex optimization problem involving the parametric constraints as objective function with the parameter as variable. In this paper we tackle the latter problem with a variant of the cutting angle method called ECAM, a global optimization procedure for solving Lipschitz programming problems. We implement different variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.

Alexander Rubinov - An outstanding scholar

**Authors:**Bagirov, Adil**Date:**2010**Type:**Text , Journal article**Relation:**Pacific Journal of Optimization Vol. 6, no. 2, Suppl. 1 (2010), p. 203-209**Full Text:**false

DC programming algorithm for clusterwise linear L1 regression

**Authors:**Bagirov, Adil , Taheri, Sona**Date:**2017**Type:**Text , Journal article**Relation:**Journal of the Operations Research Society of China Vol. 5, no. 2 (2017), p. 233-256**Relation:**http://purl.org/au-research/grants/arc/DP140103213**Full Text:**false**Reviewed:****Description:**The aim of this paper is to develop an algorithm for solving the clusterwise linear least absolute deviations regression problem. This problem is formulated as a nonsmooth nonconvex optimization problem, and the objective function is represented as a difference of convex functions. Optimality conditions are derived by using this representation. An algorithm is designed based on the difference of convex representation and an incremental approach. The proposed algorithm is tested using small to large artificial and real-world data sets. © 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.

A new nonsmooth optimization algorithm for minimum sum-of-squares clustering problems

- Bagirov, Adil, Yearwood, John

**Authors:**Bagirov, Adil , Yearwood, John**Date:**2006**Type:**Text , Journal article**Relation:**European Journal of Operational Research Vol. 170, no. 2 (2006), p. 578-596**Full Text:**false**Reviewed:****Description:**The minimum sum-of-squares clustering problem is formulated as a problem of nonsmooth, nonconvex optimization, and an algorithm for solving the former problem based on nonsmooth optimization techniques is developed. The issue of applying this algorithm to large data sets is discussed. Results of numerical experiments have been presented which demonstrate the effectiveness of the proposed algorithm. © 2004 Elsevier B.V. All rights reserved.**Description:**C1**Description:**2003001520

**Authors:**Bagirov, Adil , Ugon, Julien**Date:**2018**Type:**Text , Journal article**Relation:**Optimization Methods and Software Vol. 33, no. 1 (2018), p. 194-219**Relation:**http://purl.org/au-research/grants/arc/DP140103213**Full Text:**false**Reviewed:****Description:**The clusterwise linear regression problem is formulated as a nonsmooth nonconvex optimization problem using the squared regression error function. The objective function in this problem is represented as a difference of convex functions. Optimality conditions are derived, and an algorithm is designed based on such a representation. An incremental approach is proposed to generate starting solutions. The algorithm is tested on small to large data sets. © 2017 Informa UK Limited, trading as Taylor & Francis Group.

Comparison of metaheuristic algorithms for pump operation optimization

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

**Authors:**Bagirov, Adil , Ahmed, S. T. , Barton, Andrew , Mala-Jetmarova, Helena , Al Nuaimat, Alia , Sultanova, Nargiz**Date:**2012**Type:**Text , Conference paper**Relation:**14th Water Distribution Systems Analysis Conference 2012, WDSA 2012 Vol. 2; Adelaide, Australia; 24th-27th September 2012; p. 886-896**Relation:**http://purl.org/au-research/grants/arc/LP0990908**Full Text:**false**Reviewed:****Description:**Pumping cost constitutes the main part of the overall operating cost of water distribution systems. There are different optimization formulations of the pumping cost minimization problem including those with application of continuous and integer programming approaches. To date mainly various metaheuristics have been applied to solve this problem. However, the comprehensive comparison of those metaheuristics has not been done. Such a comparison is important to identify strengths and weaknesses of different algorithms which reflects on their performance. In this paper, we present a methodology for comparative analysis of widely used metaheuristics for solving the pumping cost minimization problem. This methodology includes the following comparison criteria: (a) the "optimal solution" obtained; (b) the efficiency; and (c) robustness. Algorithms applied are: particle swarm optimization, artificial bee colony and firefly algorithms. These algorithms were applied to one test problem available in the literature. The results obtained demonstrate that the artificial bee colony is the most robust and the firefly is the most efficient and accurate algorithm for this test problem. Funding :ARC

An algorithm for clustering based on non-smooth optimization techniques

- Bagirov, Adil, Rubinov, Alex, Sukhorukova, Nadezda, Yearwood, John

**Authors:**Bagirov, Adil , Rubinov, Alex , Sukhorukova, Nadezda , Yearwood, John**Date:**2003**Type:**Text , Journal article**Relation:**International Transactions in Operational Research Vol. 10, no. 6 (2003), p. 611-617**Full Text:**false**Reviewed:****Description:**The problem of cluster analysis is formulated as a problem of non-smooth, non-convex optimization, and an algorithm for solving the cluster analysis problem based on non-smooth optimization techniques is developed. We discuss applications of this algorithm in large databases. Results of numerical experiments are presented to demonstrate the effectiveness of this algorithm.**Description:**C1**Description:**2003000422

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.

A quasisecant method for minimizing nonsmooth functions

- Bagirov, Adil, Ganjehlou, Asef Nazari

**Authors:**Bagirov, Adil , Ganjehlou, Asef Nazari**Date:**2010**Type:**Text , Journal article**Relation:**Optimization Methods and Software Vol. 25, no. 1 (2010), p. 3-18**Relation:**http://purl.org/au-research/grants/arc/DP0666061**Full Text:**false**Reviewed:****Description:**We present an algorithm to locally minimize nonsmooth, nonconvex functions. In order to find descent directions, the notion of quasisecants, introduced in this paper, is applied. We prove that the algorithm converges to Clarke stationary points. Numerical results are presented demonstrating the applicability of the proposed algorithm to a wide variety of nonsmooth, nonconvex optimization problems. We also compare the proposed algorithm with the bundle method using numerical results.

Codifferential method for minimizing nonsmooth DC functions

**Authors:**Bagirov, Adil , Ugon, Julien**Date:**2011**Type:**Text , Journal article**Relation:**Journal of Global Optimization Vol. 50, no. 1 (2011), p. 3-22**Relation:**http://purl.org/au-research/grants/arc/DP0666061**Full Text:**false**Reviewed:****Description:**In this paper, a new algorithm to locally minimize nonsmooth functions represented as a difference of two convex functions (DC functions) is proposed. The algorithm is based on the concept of codifferential. It is assumed that DC decomposition of the objective function is known a priori. We develop an algorithm to compute descent directions using a few elements from codifferential. The convergence of the minimization algorithm is studied and its comparison with different versions of the bundle methods using results of numerical experiments is given. © 2010 Springer Science+Business Media, LLC.

- Bagirov, Adil, Miettinen, Kaisa, Weber, Gerhard-Wilhelm

**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**Reviewed:****Description:**C1

**Authors:**Bagirov, Adil , Ugon, Julien**Date:**2018**Type:**Text , Journal article**Relation:**Optimization Methods and Software Vol. 33, no. 1 (2018), p. 194-219**Full Text:**false**Reviewed:****Description:**The clusterwise linear regression problem is formulated as a nonsmooth nonconvex optimization problem using the squared regression error function. The objective function in this problem is represented as a difference of convex functions. Optimality conditions are derived, and an algorithm is designed based on such a representation. An incremental approach is proposed to generate starting solutions. The algorithm is tested on small to large data sets.

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