ON OPTIMALITY CONDITIONS FOR TRILEVEL DYNAMIC OPTIMIZATION PROBLEMS

Global Optimality Conditions for Optimization Problems∗

We establish new necessary and sufficient optimality conditions for optimization problems. In particular, we establish tractable optimality conditions for the problems of minimizing a weakly convex or concave function subject to standard constraints, such as box constraints, binary constraints, and simplex constraints. Our main theoretical tool for establishing these optimality conditions is ab...

Optimality Conditions for Constrained Optimization Problems

On -optimality Conditions for Convex Set-valued Optimization Problems

In this paper, -subgradients for convex set-valued maps are defined. We prove an existence theorem for -subgradients of convex set-valued maps. Also, we give necessary optimality conditions for an -solution of a convex set-valued optimization problem (CSP). Moreover, using the single-valued function induced from the set-valued map, we obtain theorems describing the -subgradient sum formula for ...

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...

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...