Strong Karush–Kuhn–Tucker optimality conditions for weak efficiency in constrained multiobjective programming problems in terms of mordukhovich subdifferentials

2020 ◽  
Author(s):  
Tran Van Su ◽  
Nguyen Duc Hien
Keyword(s):  
Optimality Conditions ◽  
Multiobjective Programming ◽  
Weak Efficiency ◽  
Multiobjective Programming Problems

scholarly journals Sufficiency and Duality for Multiobjective Programming under New Invexity

2016 ◽  
Vol 2016 ◽  
pp. 1-14
Author(s):  
Yingchun Zheng ◽  
Xiaoyan Gao
Keyword(s):  
Multiobjective Programming ◽  
Inequality Constraints ◽  
Weak Efficiency ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Or Efficiency ◽  
New Concepts ◽  
Multiobjective Programming Problems ◽  
Dual Models ◽  
Strong Dual

A class of multiobjective programming problems including inequality constraints is considered. To this aim, some new concepts of generalizedF,P-type I andF,P-type II functions are introduced in the differentiable assumption by using the sublinear functionF. These new functions are used to establish and prove the sufficient optimality conditions for weak efficiency or efficiency of the multiobjective programming problems. Moreover, two kinds of dual models are formulated. The weak dual, strong dual, and strict converse dual results are obtained under the aforesaid functions.

scholarly journals Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

4OR ◽  
2021 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Smooth Vector ◽  
Duality Results ◽  
Vanishing Constraints ◽  
Multiobjective Programming Problems

AbstractIn this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient optimality conditions are proved for such nonconvex smooth vector optimization problems. Further, vector duals in the sense of Mond–Weir are defined for the considered differentiable semi-infinite multiobjective programming problems with vanishing constraints and several duality results are established also under invexity hypotheses.

scholarly journals On semi-G-V-type I concepts for directionally differentiable multiobjective programming problems

2016 ◽  
Vol 6 (2) ◽  
pp. 189-203
Author(s):  
Tadeusz Antczak ◽  
Gabriel Ruiz-Garzón
Keyword(s):  
Optimality Conditions ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Invex Functions ◽  
Differentiable Functions ◽  
Necessary And Sufficient ◽  
Multiobjective Programming Problems

In this paper, a new class of nonconvex nonsmooth multiobjective programming problems with directionally differentiable functions is considered. The so-called G-V-type I objective and constraint functions and their generalizations are introduced for such nonsmooth vector optimization problems. Based upon these generalized invex functions, necessary and sufficient optimality conditions are established for directionally differentiable multiobjective programming problems. Thus, new Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions are proved for the considered directionally differentiable multiobjective programming problem. Further, weak, strong and converse duality theorems are also derived for Mond-Weir type vector dual programs.

scholarly journals Duality for a class of nonsmooth multiobjective programming problems using convexificators

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 489-498 ◽  
Author(s):  
Anurag Jayswal ◽  
Krishna Kummari ◽  
Vivek Singh
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Duality Results ◽  
Nonsmooth Multiobjective Programming ◽  
Multiobjective Programming Problem ◽  
Multiobjective Programming Problems ◽  
Dual Models

As duality is an important and interesting feature of optimization problems, in this paper, we continue the effort of Long and Huang [X. J. Long, N. J. Huang, Optimality conditions for efficiency on nonsmooth multiobjective programming problems, Taiwanese J. Math., 18 (2014) 687-699] to discuss duality results of two types of dual models for a nonsmooth multiobjective programming problem using convexificators.

Sign in / Sign up

Export Citation Format

Share Document