Second-order Optimality Conditions for Nonsmooth Multiobjective Optimization Problems

2002 ◽  
Author(s):  
Davide La Torre ◽  
Giovanni P. Crespi ◽  
Matteo Rocca
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Second Order ◽  
Second Order Optimality Conditions ◽  
Multiobjective Optimization Problems ◽  
Nonsmooth Multiobjective Optimization

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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