Optimality conditions for nonsmooth multiobjective optimization problems with general inequality constraints

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
General Inequality ◽  
Multiobjective Optimization Problems ◽  
Nonsmooth Multiobjective Optimization

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.

Generalized Convexity and Characterization of (Weak) Pareto-Optimality in Nonsmooth Multiobjective Optimization Problems

2015 ◽  
Vol 14 (04) ◽  
pp. 877-899 ◽  
Author(s):  
Majid Soleimani-Damaneh
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Nonsmooth Analysis ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Sufficient Optimality Conditions ◽  
Differential Analysis ◽  
Multiobjective Optimization Problems ◽  
Nonsmooth Multiobjective Optimization

Efforts to characterize optimality in nonsmooth and/or nonconvex optimization problems have made rapid progress in the past four decades. Nonsmooth analysis, which refers to differential analysis in the absence of differentiability, has grown rapidly in recent years, and plays a vital role in functional analysis, information technology, optimization, mechanics, differential equations, decision making, etc. Furthermore, convexity has been increasingly important nowadays in the study of many pure and applied mathematical problems. In this paper, some new connections between three major fields, nonsmooth analysis, convex analysis, and optimization, are provided that will help to make these fields accessible to a wider audience. In this paper, at first, we address some newly reported and interesting applications of multiobjective optimization in Management Science and Biology. Afterwards, some sufficient conditions for characterizing the feasible and improving directions of nonsmooth multiobjective optimization problems are given, and using these results a necessary optimality condition is proved. The sufficient optimality conditions are given utilizing a generalized convexity notion. Establishing necessary and sufficient optimality conditions for nonsmooth fractional programming problems is the next aim of the paper. We follow the paper by studying (strictly) prequasiinvexity and pseudoinvexity. Finally, some connections between these notions as well as some applications of these concepts in optimization are given.

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