optimality conditions for approximate solutions of vector optimization problems with variable ordering structures

Optimality conditions for approximate solutions of vector optimization problems with variable ordering structures

‎We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces‎. ‎Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...

Optimality Conditions for Approximate Solutions in Multiobjective Optimization Problems

We study firstand second-order necessary and sufficient optimality conditions for approximate weakly, properly efficient solutions of multiobjective optimization problems. Here, tangent cone, -normal cone, cones of feasible directions, second-order tangent set, asymptotic second-order cone, and Hadamard upper lower directional derivatives are used in the characterizations. The results are first...

Necessary Optimality Conditions for εe–Pareto Solutions in Vector Optimization with Empty Interior Ordering Cones

We present new necessary optimality conditions for εe–Pareto optimal solutions of constrained vector optimization problems with empty interior ordering cones. We use the dual-space approach based on advanced tools of variational analysis and generalized differentiation. It allows us not implement any scalarization technique while be able to establish necessary results for nonconvex and nonsolid...

Variable Ordering Structures in Vector Optimization

Properly optimal elements in vector optimization with variable ordering structures

In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions.

On Optimality Conditions for Abstract Convex Vector Optimization Problems

A sequential optimality condition characterizing the efficient solution without any constraint qualification for an abstract convex vector optimization problem is given in sequential forms using subdifferentials and 2-subdifferentials. Another sequential condition involving only the subdifferentials, but at nearby points to the efficient solution for constraints, is also derived. Moreover, we p...