Author
Nader Kanzi
Other affiliations: University of Isfahan
Bio: Nader Kanzi is an academic researcher from Payame Noor University. The author has contributed to research in topics: Semi-infinite programming & Subderivative. The author has an hindex of 10, co-authored 34 publications receiving 319 citations. Previous affiliations of Nader Kanzi include University of Isfahan.
Papers
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TL;DR: By imposing assumptions of generalized convexity, this paper gives sufficient conditions for efficient solutions for nonsmooth multiobjective semi-infinite programming problems in which the index set of the inequality constraints is an arbitrary set not necessarily finite.
Abstract: This paper is devoted to the study of nonsmooth multiobjective semi-infinite programming problems in which the index set of the inequality constraints is an arbitrary set not necessarily finite. We introduce several kinds of constraint qualifications for these problems, and then necessary optimality conditions for weakly efficient solutions are investigated. Finally by imposing assumptions of generalized convexity we give sufficient conditions for efficient solutions.
56 citations
TL;DR: Several kinds of constraint qualifications for non-smooth semi-infinite programming problems in which the index set of the inequality constraints is an arbitrary set not necessarily finite are introduced.
Abstract: This article deals with a class of non-smooth semi-infinite programming (SIP) problems in which the index set of the inequality constraints is an arbitrary set not necessarily finite. We introduce several kinds of constraint qualifications for these non-smooth SIP problems and we study the relationships between them. Finally, necessary and sufficient optimality conditions are investigated.
50 citations
TL;DR: In this article, for a nonsmooth semi-infinite programming problem where the objective and constraint functions are locally Lipschitz, analogues of the Guignard, Kuhn-Tucker, and Cottle constraint qualifications are given.
Abstract: In this paper, for a nonsmooth semi-infinite programming problem where the objective and constraint functions are locally Lipschitz, analogues of the Guignard, Kuhn-Tucker, and Cottle constraint qualifications are given. Pshenichnyi-Levin-Valadire property is introduced, and Karush-Kuhn-Tucker type necessary optimality conditions are derived.
43 citations
TL;DR: In this article, the authors considered a nonsmooth semi-infinite programming problem with a feasible set defined by inequality and equality constraints and a set constraint, and applied alternative theorems to obtain, under different constraint qualifications, several necessary optimality conditions in the type of Fritz-John and Karush-Kuhn-Tucker.
30 citations
TL;DR: New and already known data qualifications are introduced in order to get optimality conditions which are expressed in terms of either Karusk–Kuhn–Tucker multipliers or a new gap function associated with the given problem.
Abstract: The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely many convex constraints. To do this, we introduce new and already known data qualifications (conditions involving the constraints and/or the objectives) in order to get optimality conditions which are expressed in terms of either Karusk---Kuhn---Tucker multipliers or a new gap function associated with the given problem.
26 citations
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TL;DR: This article surveys recent developments in theory and numerical methods for standard and generalized semi-infinite optimization problems, paying particular attention to connections with mathematical programs with complementarity constraints, lower level Wolfe duality, semi-smooth approaches, as well as branch and bound techniques in adaptive convexification procedures.
105 citations
TL;DR: Some advanced tools of variational analysis and generalized differentiation are applied to establish necessary conditions for (weakly) efficient solutions of a nonsmooth semi-infinite multiobjective optimization problem (SIMOP for brevity).
Abstract: We apply some advanced tools of variational analysis and generalized differentiation to establish necessary conditions for (weakly) efficient solutions of a nonsmooth semi-infinite multiobjective optimization problem (SIMOP for brevity). Sufficient conditions for (weakly) efficient solutions of a SIMOP are also provided by means of introducing the concepts of (strictly) generalized convex functions defined in terms of the limiting subdifferential of locally Lipschitz functions. In addition, we propose types of Wolfe and Mond–Weir dual problems for SIMOPs, and explore weak and strong duality relations under assumptions of (strictly) generalized convexity. Examples are also designed to analyze and illustrate the obtained results.
64 citations