Approximate Solutions for Multi-Objective Optimization Problems via Scalarizing and Nonscalarizing Methods

In this paper, max-ordering and weighted compromising methods are employed to investigate approximate Pareto solutions for a class of multi-objective optimization problems with an infinite number of constraints. Approximate optimality conditions for ε-quasi Pareto solutions and almost ε-quasi Pareto solutions of the considered problems are established. The results are derived using a new notion of ε-quasi subdifferen tials for locally Lipschitz functions and ε-quasi normal sets. Approximate duality theorems are also introduced. In particular, the relationships between the original multi-objective optimization problem and its dual are ana lyzed via a corresponding pair of primal-dual scalar problems. Several examples are provided to illustrate the proposed notions and to demonstrate the applicability of the obtained results