scholarly journals Generalized Constraint Qualifications and Optimality Conditions for Set-Valued Optimization Problems

2002 ◽  
Vol 265 (2) ◽  
pp. 309-321 ◽  
Author(s):  
Huang Yong-Wei
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Generalized Constraint

scholarly journals Strong complementary approximate Karush-Kuhn-Tucker conditions for multiobjective optimization problems

2021 ◽  
pp. 24-24
Author(s):  
Jitendra Maurya ◽  
Shashi Mishra
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
Multiobjective Optimization Problems ◽  
Sequential Optimality Conditions ◽  
Equality And Inequality Constraints ◽  
Optim Theory

In this paper, we establish strong complementary approximate Karush- Kuhn-Tucker (SCAKKT) sequential optimality conditions for multiobjective optimization problems with equality and inequality constraints without any constraint qualifications and introduce a weak constraint qualification which assures the equivalence between SCAKKT and the strong Karush-Kuhn-Tucker (J Optim Theory Appl 80 (3): 483{500, 1994) conditions for multiobjective optimization problems.

scholarly journals CQ-free optimality conditions and strong dual formulations for a special conic optimization problem

2020 ◽  
Vol 8 (3) ◽  
pp. 668-683
Author(s):  
Olga Kostyukova ◽  
Tatiana V. Tchemisova
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Strong Duality ◽  
Conic Optimization ◽  
First Order ◽  
Primal And Dual ◽  
Linear Cost ◽  
Strong Dual

In this paper, we consider a special class of conic optimization problems, consisting of set-semidefinite(or K-semidefinite) programming problems, where the set K is a polyhedral convex cone. For these problems, we introduce the concept of immobile indices and study the properties of the set of normalized immobile indices and the feasible set. This study provides the main result of the paper, which is to formulate and prove the new first-order optimality conditions in the form of a criterion. The optimality conditions are explicit and do not use any constraint qualifications. For the case of a linear cost function, we reformulate the K-semidefinite problem in a regularized form and construct its dual. We show that the pair of the primal and dual regularized problems satisfies the strong duality relation which means that the duality gap is vanishing.

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