Nonsmooth semi-infinite programming problems with mixed constraints

Kanzi, Nader; Nobakhtian, S.

doi:10.1016/j.jmaa.2008.10.009

Cited by 27 publications

(15 citation statements)

References 12 publications

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“…This is due to the fact that several engineering problems lead to SIP; see [1,5,14]. Optimality conditions of SIP problems have been studied by many authors; see for instance [1,14] in linear case, [15,19,20,21] in convex case, [5] in smooth case, and [7,8,9,10,29] in locally Lipschitz case.…”

Section: Introductionmentioning

confidence: 99%

Slater CQ, optimality and duality for quasiconvex semi-infinite optimization problems

Kanzi

Soleimani-damaneh

2016

Journal of Mathematical Analysis and Applications

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Please cite this article in press as: N. Kanzi, M. Soleimani-damaneh, Slater CQ, optimality and duality for quasiconvex semi-infinite optimization problems, J. Math. Anal. Appl. (2015), http://dx. AbstractIn this paper, we introduce and study the Slater constraint qualification (CQ) for a semi-infinite optimization problem with upper-semicontinuous quasiconvex objective and constraint functions. Then, some Karush-KuhnTucker (KKT) type necessary and sufficient optimality conditions as well as duality results are derived. The final part of the paper is devoted to a linear characterization of optimality and the gap function for considered semi-infinite problem.

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Section: Introductionmentioning

confidence: 99%

Slater CQ, optimality and duality for quasiconvex semi-infinite optimization problems

Kanzi

Soleimani-damaneh

2016

Journal of Mathematical Analysis and Applications

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“…Recently, Qingxiang zhang [13] obtained the necessary and sufficient optimality conditions for the nondifferentiable nonlinear semi-infinite programming involving B-arcwise connected functions. In [14,15,16,17], the optimality conditions under various constraints qualification for semi-infinite programming problems were established.…”

Section: Introductionmentioning

confidence: 99%

Optimality and Duality for Minimax Fractional Semi-Infinite Programming

Gao¹

2013

JNW

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The purpose of this paper is to consider a class of nonsmooth minimax fractional semi-infinite programming problem. Based on the concept of tangent derivative, a new generalization of convexity, namely generalized uniform invexity, is defined for this problem. For such semi-infinite programming problem, several sufficient optimality conditions are established and proved by utilizing the above defined new classes of functions. The results extend and improve the corresponding results in the literature. Subsequently, these optimality conditions are utilized as a basis for formulating dual problems. Weak, strong and reverse duality theorems are also derived for dual programs, using generalized invexity on the functions involved. Some previous duality results for differentiable minimax fractional programming problems turn out to be special cases for the results described in the pape

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“…To date, many authors investigated the optimality conditions and duality results for semi-infinite programming problems. In particular, Kanzi and Nobakhtian [3] established some alternative theorems and several necessary optimality conditions of Fritz-John and Karush-Kuhn-Tucher type for nonsmooth semi-infinite programming problem. In [4], they also established necessary and sufficient optimality conditions under various constraints qualifications for nonsmooth semi-infinite programming problem using Clarke subdifferential.…”

Section: Introductionmentioning

confidence: 99%

Optimality and Duality for Non-smooth Multiple Objective Semi-infinite Programming

Gao¹

2013

JNW

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The purpose of this paper is to consider a class of non-smooth multiobjective semi-infinite programming problem. Based on the concepts of local cone approximation, directional derivative and subdifferential, a new generalization of convexity, namely generalized uniform convexity, is defined for this problem. For such semi-infinite programming problem, several sufficient optimality conditions are established and proved by utilizing the above defined new classes of functions. The results extend and improve the corresponding results in the literature. Subsequently, these optimality conditions are utilized as a basis for formulating dual problems. Weak, strong and reverse duality theorems are also derived for Mond-Weir type multiobjective dual programs, using generalized invexity on the functions involved. Some previous duality results for differentiable multiobjective programming problems turn out to be special cases for the results described in the paper

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Nonsmooth semi-infinite programming problems with mixed constraints

Cited by 27 publications

References 12 publications

Slater CQ, optimality and duality for quasiconvex semi-infinite optimization problems

Slater CQ, optimality and duality for quasiconvex semi-infinite optimization problems

Optimality and Duality for Minimax Fractional Semi-Infinite Programming

Optimality and Duality for Non-smooth Multiple Objective Semi-infinite Programming

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