scholarly journals Invex optimisation problems

1992 ◽  
Vol 46 (1) ◽  
pp. 47-66 ◽  
Author(s):  
D.T. Luc ◽  
C. Malivert
Keyword(s):  
Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Dual Problems ◽  
Invex Set ◽  
Duality Property ◽  
Wolfe Type Dual ◽  
Necessary And Sufficient

In this paper we extend the concept of invexity to set-valued maps and study vector optimisation problems with invex set-valued data. Necessary and sufficient optimality conditions are established in terms of contingent derivatives. Wolfe type dual problems are constructed via two recently developed approaches which guarantee the zero-gap duality property.

scholarly journals Optimality and duality in set-valued optimization utilizing limit sets

2018 ◽  
Vol 16 (1) ◽  
pp. 1128-1139
Author(s):  
Xiangyu Kong ◽  
Yinfeng Zhang ◽  
GuoLin Yu
Keyword(s):  
Optimality Conditions ◽  
Duality Theory ◽  
Optimization Problem ◽  
Convex Set ◽  
Sufficient Optimality Conditions ◽  
Constraint Optimization ◽  
Limit Sets ◽  
Optimality And Duality ◽  
Wolfe Type Dual ◽  
Necessary And Sufficient

AbstractThis paper deals with optimality conditions and duality theory for vector optimization involving non-convex set-valued maps. Firstly, under the assumption of nearly cone-subconvexlike property for set-valued maps, the necessary and sufficient optimality conditions in terms of limit sets are derived for local weak minimizers of a set-valued constraint optimization problem. Then, applications to Mond-Weir type and Wolfe type dual problems are presented.

On nondifferentiable minimax semi-infinite programming problems in complex spaces

2016 ◽  
Vol 23 (3) ◽  
pp. 367-380
Author(s):  
Anurag Jayswal ◽  
Krishna Kummari
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Complex Space ◽  
Sufficient Optimality Conditions ◽  
Dual Problems ◽  
Complex Spaces ◽  
Infinite Programming ◽  
Primal And Dual Problems ◽  
Primal And Dual ◽  
Necessary And Sufficient

AbstractThe purpose of this paper is to study a nondifferentiable minimax semi-infinite programming problem in a complex space. For such a semi-infinite programming problem, necessary and sufficient optimality conditions are established by utilizing the invexity assumptions. Subsequently, these optimality conditions are utilized as a basis for formulating dual problems. In order to relate the primal and dual problems, we have also derived appropriate duality theorems.

scholarly journals A note on the paper "Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints"

2021 ◽  
Author(s):  
Nazih Abderrazzak Gadhi
Keyword(s):  
Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Equilibrium Constraints ◽  
Mathematical Programs ◽  
Necessary And Sufficient

In this work, some counterexamples are given to refute some results in the paper by Kohli (RAIRO-Oper. Res. 53, 1617-1632, 2019). We correct the faulty in some of his results.

scholarly journals Strict lower subdifferentiability and applications

1999 ◽  
Vol 40 (3) ◽  
pp. 379-391 ◽  
Author(s):  
H. Xu ◽  
A. M. Rubinov ◽  
B. M. Glover
Keyword(s):  
Global Convergence ◽  
Optimality Conditions ◽  
Convex Subset ◽  
Sufficient Optimality Conditions ◽  
Descent Direction ◽  
Minimization Problems ◽  
Convergence Results ◽  
Lower Subdifferential ◽  
Necessary And Sufficient ◽  
Convex Subdifferential

AbstractWe investigate the strict lower subdifferentiability of a real-valued function on a closed convex subset of Rn. Relations between the strict lower subdifferential, lower subdifferential, and the usual convex subdifferential are established. Furthermore, we present necessary and sufficient optimality conditions for a class of quasiconvex minimization problems in terms of lower and strict lower subdifferentials. Finally, a descent direction method is proposed and global convergence results of the consequent algorithm are obtained.

scholarly journals Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 12 ◽  
Author(s):  
Xiangkai Sun ◽  
Hongyong Fu ◽  
Jing Zeng
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Sufficient Optimality Conditions ◽  
Convex Constraint ◽  
Approximate Optimality Conditions ◽  
Necessary And Sufficient

This paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by using the robust type closed convex constraint qualification and robust optimization technique, we obtain some necessary and sufficient optimality conditions for robust quasi approximate optimal solution and exact optimal solution of this nonsmooth uncertain semi-infinite optimization problem. Moreover, the obtained results in this paper are applied to a nonsmooth uncertain optimization problem with cone constraints.

scholarly journals Duality and Lagrange multipliers for nonsmooth multiobjective programming

2006 ◽  
Vol 74 (3) ◽  
pp. 369-383 ◽  
Author(s):  
Houchun Zhou ◽  
Wenyu Sun
Keyword(s):  
Optimality Conditions ◽  
Lagrange Multipliers ◽  
Constraint Qualification ◽  
Multiobjective Programming ◽  
Sufficient Optimality Conditions ◽  
Dual Model ◽  
Mixed Duality ◽  
Nonsmooth Multiobjective Programming ◽  
Necessary And Sufficient ◽  
Dual Models

Without any constraint qualification, the necessary and sufficient optimality conditions are established in this paper for nonsmooth multiobjective programming involving generalised convex functions. With these optimality conditions, a mixed dual model is constructed which unifies two dual models. Several theorems on mixed duality and Lagrange multipliers are established in this paper.

scholarly journals Higher-order optimality conditions for a minimax

1996 ◽  
Vol 54 (3) ◽  
pp. 509-516 ◽  
Author(s):  
Do Van Luu ◽  
W. Oettli
Keyword(s):  
Optimality Conditions ◽  
Minimax Problem ◽  
Higher Order ◽  
Regularity Conditions ◽  
Sufficient Optimality Conditions ◽  
Basic Assumptions ◽  
Necessary And Sufficient ◽  
Inequality Type

Higher-order necessary and sufficient optimality conditions for a nonsmooth minimax problem with infinitely many constraints of inequality type are established under suitable basic assumptions and regularity conditions.

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