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28Bagirov, Adil
25Gao, David
23Kruger, Alexander
18López, Marco
15Wu, Zhiyou
14Rubinov, Alex
13Gunawan, Indra
13Mammadov, Musa
13Roshchina, Vera
13Ugon, Julien
11Outrata, Jiri
9Sukhorukova, Nadezda
7Goberna, Miguel
6Bai, Fusheng
6Ooi, Ean Tat
6Yearwood, John
5Dinh, Nguyen
5Song, Chongmin
5Taheri, Sona
5Thao, Nguyen

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1220103 Numerical and Computational Mathematics
350802 Computation Theory and Mathematics
350906 Electrical and Electronic Engineering
210101 Pure Mathematics
20Global optimization
180905 Civil Engineering
18Nonsmooth optimization
140913 Mechanical Engineering
120801 Artificial Intelligence and Image Processing
12Subdifferential
11Nonconvex optimization
101202 Building
10Metric regularity
8Canonical duality theory
7Optimization
6Error bounds
6Optimality conditions
5Algorithms
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- Wu, Zhiyou, Bai, Fusheng, Tian, Jing

**Authors:**Wu, Zhiyou , Bai, Fusheng , Tian, Jing**Date:**2017**Type:**Text , Journal article**Relation:**Journal of the Operations Research Society of China Vol. 5, no. 2 (2017), p. 193-218**Full Text:**false**Reviewed:****Description:**In this paper, an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials. Based on this condition, two new local optimization methods are developed. The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker (KKT) points in general. Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method. Some numerical examples are reported to show the effectiveness of the proposed methods. © 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.

Outer approximation schemes for generalized semi-infinite variational inequality problems

**Authors:**Burachik, Regina , Lopes, J.**Date:**2010**Type:**Text , Journal article**Relation:**Optimization Vol. 59, no. 4 (2010), p. 601-617**Full Text:**false**Reviewed:****Description:**We introduce and analyse outer approximation schemes for solving variational inequality problems in which the constraint set is as in generalized semi-infinite programming. We call these problems generalized semi-infinite variational inequality problems. First, we establish convergence results of our method under standard boundedness assumptions. Second, we use suitable Tikhonov-like regularizations for establishing convergence in the unbounded case.

Outer limits of subdifferentials for min–max type functions

- Eberhard, Andrew, Roshchina, Vera, Sang, Tian

**Authors:**Eberhard, Andrew , Roshchina, Vera , Sang, Tian**Date:**2019**Type:**Text , Journal article**Relation:**Optimization Vol. 68, no. 7 (2019), p. 1391-1409**Full Text:****Reviewed:****Description:**We generalize the outer subdifferential construction suggested by Cánovas, Henrion, López and Parra for max type functions to pointwise minima of regular Lipschitz functions. We also answer an open question about the relation between the outer subdifferential of the support of a regular function and the end set of its subdifferential posed by Li, Meng and Yang.

**Authors:**Eberhard, Andrew , Roshchina, Vera , Sang, Tian**Date:**2019**Type:**Text , Journal article**Relation:**Optimization Vol. 68, no. 7 (2019), p. 1391-1409**Full Text:****Reviewed:****Description:**We generalize the outer subdifferential construction suggested by Cánovas, Henrion, López and Parra for max type functions to pointwise minima of regular Lipschitz functions. We also answer an open question about the relation between the outer subdifferential of the support of a regular function and the end set of its subdifferential posed by Li, Meng and Yang.

- Wen, S. P, Zeng, Z., Huang, Tingwen, Li, Chaojie

**Authors:**Wen, S. P , Zeng, Z. , Huang, Tingwen , Li, Chaojie**Date:**2015**Type:**Text , Journal article**Relation:**International Journal of Robust and Nonlinear Control Vol. 25, no. 4 (2015), p. 610-624**Full Text:**false**Reviewed:****Description:**This paper is concerned with the problem of passivity analysis and passification for a class of stochastic impulsive memristor-based piecewise linear (PWL) systems with mixed delays and nonlinearity disturbances. Based on the PWL memristor, a PWL system is set up. And some novel sufficient conditions are derived to ensure the passivity/passification performance, such that, for all admissible stochastic disturbances and nonlinearity, the closed-loop stochastic impulsive memristor-based PWL system is passive in the sense of expectation. Copyright (c) 2013 John Wiley & Sons, Ltd.

Perturbation of error bounds

- Kruger, Alexander, López, Marco, Théra, Michel

**Authors:**Kruger, Alexander , López, Marco , Théra, Michel**Date:**2018**Type:**Text , Journal article**Relation:**Mathematical Programming Vol. 168, no. 1-2 (2018), p. 533-554**Relation:**http://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**Our aim in the current article is to extend the developments in Kruger et al. (SIAM J Optim 20(6):3280–3296, 2010. doi:10.1137/100782206) and, more precisely, to characterize, in the Banach space setting, the stability of the local and global error bound property of inequalities determined by lower semicontinuous functions under data perturbations. We propose new concepts of (arbitrary, convex and linear) perturbations of the given function defining the system under consideration, which turn out to be a useful tool in our analysis. The characterizations of error bounds for families of perturbations can be interpreted as estimates of the ‘radius of error bounds’. The definitions and characterizations are illustrated by examples. © 2017, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

**Authors:**Kruger, Alexander , López, Marco , Théra, Michel**Date:**2018**Type:**Text , Journal article**Relation:**Mathematical Programming Vol. 168, no. 1-2 (2018), p. 533-554**Relation:**http://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**Our aim in the current article is to extend the developments in Kruger et al. (SIAM J Optim 20(6):3280–3296, 2010. doi:10.1137/100782206) and, more precisely, to characterize, in the Banach space setting, the stability of the local and global error bound property of inequalities determined by lower semicontinuous functions under data perturbations. We propose new concepts of (arbitrary, convex and linear) perturbations of the given function defining the system under consideration, which turn out to be a useful tool in our analysis. The characterizations of error bounds for families of perturbations can be interpreted as estimates of the ‘radius of error bounds’. The definitions and characterizations are illustrated by examples. © 2017, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

Post-buckling solutions of hyper-elastic beam by canonical dual finite element method

- Cai, Kun, Gao, David, Qin, Qing

**Authors:**Cai, Kun , Gao, David , Qin, Qing**Date:**2014**Type:**Text , Journal article**Relation:**Mathematics and Mechanics of Solids Vol. 19, no. 6 (2014), p. 659-671**Full Text:**false**Reviewed:****Description:**The post-buckling problem of a large deformed beam is analyzed using the canonical dual finite element method (CD-FEM). The feature of this method is to choose correctly the canonical dual stress so that the original non-convex potential energy functional is reformulated in a mixed complementary energy form with both displacement and stress fields, and a pure complementary energy is explicitly formulated in finite dimensional space. Based on the canonical duality theory and the associated triality theorem, a primal–dual algorithm is proposed, which can be used to find all possible solutions of this non-convex post-buckling problem. Numerical results show that the global maximum of the pure-complementary energy leads to a stable buckled configuration of the beam, while the local extrema of the pure-complementary energy present unstable deformation states. We discovered that the unstable buckled state is very sensitive to the number of total elements and the external loads. Theoretical results are verified through numerical examples and some interesting phenomena in post-bifurcation of this large deformed beam are observed.

- Weber, Gerhard-Wilhelm, Çavu, Özmen, Ay

**Authors:**Weber, Gerhard-Wilhelm , Çavu , Özmen, Ay**Date:**2012**Type:**Text , Journal article**Relation:**Optimization Vol. 61, no. 4 (2012), p. 443-457**Full Text:**false**Reviewed:****Description:**Nowadays, the importance of financial crises and defaults of countries are becoming clear due to the globalization in the economic area and investments. Generalized partial linear model (GPLM) is a combination of two different regression models connecting with the mean of the dependent variable with the help of a link function. It is adequate to high-dimensional, non-normal data sets having the flexibility to reflect all anomalies effectively. The nonlinear patterns are also easily explained by the nonparametric component of the model. In this study, we introduce a newly developed conic GPLM (CGPLM) to predict default probabilities of 45 emerging markets using the contribution of a continuous model CMARS and a discrete model logistic regression. We present its application results on a data set with 13 macroeconomic variables in 25 years' time. To predict debt crises, CGPLM gives better results than a single CMARS and a single logistic regression. In fact, we have 91.81% and 89.31% accuracy rates, computed according to the correctness of the model output, for training and validation sample, respectively. This improvement in prediction of crises can contribute to new prospects and developments in financial mathematics to make more accurate previsions for investments and to take measures due to coming risks. © 2012 Copyright Taylor and Francis Group, 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

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

Quadratic form representations via generalized continuants

- Delorme, Charles, Pineda-Villavicencio, Guillermo

**Authors:**Delorme, Charles , Pineda-Villavicencio, Guillermo**Date:**2015**Type:**Text , Journal article**Relation:**Journal of Integer Sequences Vol. 18, no. 6 (2015), p. Article number 15.6.4**Full Text:**false**Reviewed:****Description:**H. J. S. Smith proved Fermat’s two-square theorem using the notion of palindromic continuants. In this paper we extend Smith’s approach to proper binary quadratic form representations in some commutative Euclidean rings, including rings of integers and rings of polynomials over fields of odd characteristic. Also, we present new deterministic algorithms for finding the corresponding proper representations. © 2015 University of Waterloo. All rights reserved.

Quantitative characterizations of regularity properties of collections of sets

- Kruger, Alexander, Thao, Nguyen

**Authors:**Kruger, Alexander , Thao, Nguyen**Date:**2015**Type:**Text , Journal article**Relation:**Journal of Optimization Theory and Applications Vol. 164, no. 1 (2015), p. 41-67**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**Several primal and dual quantitative characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are provided.

**Authors:**Kruger, Alexander , Thao, Nguyen**Date:**2015**Type:**Text , Journal article**Relation:**Journal of Optimization Theory and Applications Vol. 164, no. 1 (2015), p. 41-67**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**Several primal and dual quantitative characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are provided.

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

- Cánovas, Maria, López, Marco, Mordukhovich, Borris, Parra, Juan

**Authors:**Cánovas, Maria , López, Marco , Mordukhovich, Borris , Parra, Juan**Date:**2012**Type:**Text , Journal article**Relation:**TOP Vol. 20, no. 2 (2012), p. 310-327**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel-Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system's data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504-1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system's coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

**Authors:**Cánovas, Maria , López, Marco , Mordukhovich, Borris , Parra, Juan**Date:**2012**Type:**Text , Journal article**Relation:**TOP Vol. 20, no. 2 (2012), p. 310-327**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel-Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system's data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504-1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system's coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

- Gasi, Ochal, Anna, Shillor, Meir

**Authors:**Gasi , Ochal, Anna , Shillor, Meir**Date:**2016**Type:**Text , Journal article**Relation:**Nonlinear Analysis: Real World Applications Vol. 27, no. (2016), p. 183-202**Full Text:**false**Reviewed:****Description:**This paper presents and analyzes a model for quasistatic frictional contact between a thermoviscoelastic body and a moving foundation that involves wear of the contacting surface and the diffusion of the wear debris. The constitutive law includes temperature effects and the evolution of the temperature is described by a parabolic equation with a subdifferential heat exchange boundary condition. Contact is modeled with normal compliance together with a subdifferential frictional law. The rate of wear of the contact surface is described by the differential form of the Archard condition. The effects of the diffusion of the wear particles on the contact surface are taken into account. Such situations arise in mechanical joints and in orthopedic biomechanics where the wear debris is trapped, diffuses and influences the properties of joint prosthesis and implants. The variational formulation of the problem leads to a system with a time-dependent hemivariational inequality for the displacement, a parabolic hemivariational inequality for the temperature and a parabolic equation on the contact boundary for the wear diffusion. The existence of a unique weak solution is proved by using recent results from the theory of hemivariational inequalities, variational diffusion equation, and a fixed point argument. © 2015 Elsevier Ltd.

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

Recent contributions to linear semi-infinite optimization

- Goberna, Miguel, López, Marco

**Authors:**Goberna, Miguel , López, Marco**Date:**2017**Type:**Text , Journal article**Relation:**4OR: A Quarterly Journal of Operations Research Vol. 15, no. 3 (2017), p. 221-264**Relation:**http://purl.org/au-research/grants/arc/DP160100854**Full Text:**false**Reviewed:****Description:**This paper reviews the state-of-the-art in the theory of deterministic and uncertain linear semi-infinite optimization, presents some numerical approaches to this type of problems, and describes a selection of recent applications in a variety of fields. Extensions to related optimization areas, as convex semi-infinite optimization, linear infinite optimization, and multi-objective linear semi-infinite optimization, are also commented. © 2017, Springer-Verlag GmbH Germany.

Redundant paths and reliability bounds in gamma networks

**Authors:**Gunawan, Indra**Date:**2008**Type:**Text , Journal article**Relation:**Applied Mathematical modelling Vol. 32, no. (2008 2008), p. 588-594**Full Text:**false**Reviewed:****Description:**Multistage Interconnection Networks (MINs) are network systems providing fast and efficient communications at a reasonable cost. A gamma network is a specific class of MINs, which provides redundant paths in the system. In a gamma network, information from source nodes is transmitted through a specific set of routes to destination nodes. Reliability of an MIN is used as a measure of system’s ability to transform information from input to output devices. Due to the complexity of network configuration and availability of redundant paths, reliability bounds to estimate the exact reliability of a gamma network is proposed. A numerical example of an 8 × 8 gamma network is presented to demonstrate the accuracy of the reliability bounds. When the lower bound reliability provides sufficient assurance that the system will be operational at some specified time and closely approximates the exact reliability, then no further effort for obtaining the exact reliability expression is necessary.

ROI engine : return on investment model for the implementation of maintenance best practices

- Maffre, Julien, Probst, Rob, Gunawan, Indra, Neitzert, Thomas

**Authors:**Maffre, Julien , Probst, Rob , Gunawan, Indra , Neitzert, Thomas**Date:**2008**Type:**Text , Conference paper**Relation:**Proceedings of the Society for Maintenance and Reliability Professionals (SMRP) Annual Conference**Full Text:**false**Reviewed:**

Second-order variational analysis in conic programming with applications to optimality and stability

- Mordukhovich, Boris, Outrata, Jiri, Ramírez, Hector

**Authors:**Mordukhovich, Boris , Outrata, Jiri , Ramírez, Hector**Date:**2015**Type:**Text , Journal article**Relation:**SIAM Journal on Optimization Vol. 25, no. 1 (2015), p. 76-101**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**This paper is devoted to the study of a broad class of problems in conic programming modeled via parameter-dependent generalized equations. In this framework we develop a second-order generalized differential approach of variational analysis to calculate appropriate derivatives and coderivatives of the corresponding solution maps. These developments allow us to resolve some important issues related to conic programming. They include verifiable conditions for isolated calmness of the considered solution maps, sharp necessary optimality conditions for a class of mathematical programs with equilibrium constraints, and characterizations of tilt-stable local minimizers for cone-constrained problems. The main results obtained in the general conic programming setting are specified for and illustrated by the second-order cone programming. © 2015 Society for Industrial and Applied Mathematics.

**Authors:**Mordukhovich, Boris , Outrata, Jiri , Ramírez, Hector**Date:**2015**Type:**Text , Journal article**Relation:**SIAM Journal on Optimization Vol. 25, no. 1 (2015), p. 76-101**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**This paper is devoted to the study of a broad class of problems in conic programming modeled via parameter-dependent generalized equations. In this framework we develop a second-order generalized differential approach of variational analysis to calculate appropriate derivatives and coderivatives of the corresponding solution maps. These developments allow us to resolve some important issues related to conic programming. They include verifiable conditions for isolated calmness of the considered solution maps, sharp necessary optimality conditions for a class of mathematical programs with equilibrium constraints, and characterizations of tilt-stable local minimizers for cone-constrained problems. The main results obtained in the general conic programming setting are specified for and illustrated by the second-order cone programming. © 2015 Society for Industrial and Applied Mathematics.

Separation properties via connectedness of topological convexity spaces

**Authors:**Sharikov, Evgeny**Date:**2010**Type:**Text , Journal article**Relation:**Pacific Journal of Optimization Vol. 6, no. 2, Suppl. 1 (2010), p. 227-241**Full Text:**false**Description:**For a given collection H of subsets of a set X we examine the convexity on X generated by H. We use a special type of connectedness of H and X for investigation of separation of convex sets by elements of H. In particular, we give a description of convex sets, which can be represented as the intersection of a subfamily of H. As an application, we give a description of abstract convex functions and sets. We also describe the abstract convex hull of a finite union of abstract convex sets.

Set regularities and feasibility problems

- Kruger, Alexander, Luke, Russell, Thao, Nguyen

**Authors:**Kruger, Alexander , Luke, Russell , Thao, Nguyen**Date:**2018**Type:**Text , Journal article**Relation:**Mathematical Programming Vol. 168, no. 1-2 (2018), p. 279-311**Relation:**http://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of regularities are presented which shed light on the relations between seemingly different ideas and point to possible necessary conditions for local linear convergence of fundamental algorithms

**Authors:**Kruger, Alexander , Luke, Russell , Thao, Nguyen**Date:**2018**Type:**Text , Journal article**Relation:**Mathematical Programming Vol. 168, no. 1-2 (2018), p. 279-311**Relation:**http://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of regularities are presented which shed light on the relations between seemingly different ideas and point to possible necessary conditions for local linear convergence of fundamental algorithms

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