Approximations of objective function and constraints in bi-criteria optimization problems

Abstract

In this paper we study approximation methods for solving bi-criteria optimization problems. Initial problem is approximated by a new one which has the components of the objective and the constraints are replaced by their approximation functions. Components of the objective function are first and second order approximated and constraints are first order approximated. Conditions such that efficient solution of the approximate problem will remain efficient for initial problem and reciprocally are studied. Numerical examples are developed to emphasize the importance of these conditions.

Keywords

• efficient solution
• bi-criteria optimization
• eta-approximation
• invex function
• incave function
• optimization