Robust Optimality Conditions for a Class of Fractional 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

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...

Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems

One of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and on the constraint set.The present work is concerned with the co...

Global Optimization Algorithms for a Class of Fractional Programming Problems

This paper addresses the problem of minimizing a sum of fractional functions over a convex set, where each fractional function is described by the ratio between a convex and a concave function. Linear-fractional programming problems fall into this category as important special cases. Two global optimization algorithms based on a suitable reformulation of the problem in the outcome space are pro...