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.

A note on second-order Karush–Kuhn–Tucker necessary optimality conditions for smooth vector optimization problems

2018 ◽  
Vol 52 (2) ◽  
pp. 567-575 ◽  
Author(s):  
Do Sang Kim ◽  
Nguyen Van Tuyen
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Second Order ◽  
Vector Optimization Problems ◽  
Smooth Vector ◽  
Incorrect Result

The aim of this note is to present some second-order Karush–Kuhn–Tucker necessary optimality conditions for vector optimization problems, which modify the incorrect result in ((10), Thm. 3.2).

Necessary and sufficient optimality conditions for set-valued optimization problems

2011 ◽  
Vol 18 (1) ◽  
pp. 53-66
Author(s):  
Najia Benkenza ◽  
Nazih Gadhi ◽  
Lahoussine Lafhim
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Necessary And Sufficient ◽  
First Time ◽  
Funct Anal

Abstract Using a special scalarization employed for the first time for the study of necessary optimality conditions in vector optimization by Ciligot-Travain [Numer. Funct. Anal. Optim. 15: 689–693, 1994], we give necessary optimality conditions for a set-valued optimization problem by establishing the existence of Lagrange–Fritz–John multipliers. Also, sufficient optimality conditions are given without any Lipschitz assumption.

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.

scholarly journals E-invexity and generalized E-invexity in E-differentiable multiobjective programming

2019 ◽  
Vol 24 ◽  
pp. 01002 ◽  
Author(s):  
Najeeb Abdulaleem
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Differentiable Function ◽  
Generalized Convexity ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Vector Optimization Problems ◽  
Invex Functions ◽  
Differentiable Vector

In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable vector optimization problems. For an E-differentiable function, the concept of E-invexity is introduced as a generalization of the E-differentiable E-convexity notion. In addition, some properties of E-differentiable E-invex functions are investigated. Furthermore, the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable vector optimization problems with both inequality and equality constraints. Also, the sufficiency of the E-Karush-Kuhn-Tucker necessary optimality conditions are proved for such E-differentiable vector optimization problems in which the involved functions are E-invex and/or generalized E-invex.

scholarly journals Minimum Principle-Type Necessary Optimality Conditions in Scalar and Vector Optimization. An Account

2017 ◽  
Vol 9 (4) ◽  
pp. 168
Author(s):  
Giorgio Giorgi
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Minimum Principle ◽  
Necessary Optimality Conditions ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Scalar Optimization ◽  
Scalar And Vector Optimization

We take into condideration necessary optimality conditions of minimum principle-type, that is for optimization problems having, besides the usual inequality and/or equality constraints, a set constraint. The first part pf the paper is concerned with scalar optimization problems; the second part of the paper deals with vector optimization problems.

scholarly journals Nonsmooth Vector Optimization Problem Involving Second-Order Semipseudo, Semiquasi Cone-Convex Functions

2020 ◽  
Vol 9 (2) ◽  
pp. 383-398
Author(s):  
Sunila Sharma ◽  
Priyanka Yadav
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Convex Functions ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Duality Results ◽  
Nonsmooth Vector Optimization ◽  
Second Order Cone

Recently, Suneja et al. [26] introduced new classes of second-order cone-(η; ξ)-convex functions along with theirgeneralizations and used them to prove second-order Karush–Kuhn–Tucker (KKT) type optimality conditions and duality results for the vector optimization problem involving first-order differentiable and second-order directionally differentiable functions. In this paper, we move one step ahead and study a nonsmooth vector optimization problem wherein the functions involved are first and second-order directionally differentiable. We introduce new classes of nonsmooth second-order cone-semipseudoconvex and nonsmooth second-order cone-semiquasiconvex functions in terms of second-order directional derivatives. Second-order KKT type sufficient optimality conditions and duality results for the same problem are proved using these functions.

scholarly journals Higher order optimality and duality in fractional vector optimization over cones

2017 ◽  
Vol 48 (3) ◽  
pp. 273-287 ◽  
Author(s):  
Muskan Kapoor ◽  
Surjeet Kaur Suneja ◽  
Meetu Bhatia Grover
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Convex Functions ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Dual Program ◽  
Duality Results ◽  
Optimality And Duality

In this paper we give higher order sufficient optimality conditions for a fractional vector optimization problem over cones, using higher order cone-convex functions. A higher order Schaible type dual program is formulated over cones.Weak, strong and converse duality results are established by using the higher order cone convex and other related functions.

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