An algorithm for solving the problem of convex programming with several objective functions

Abstract

This work aims to establish an algorithm for solving the problem of convex programming with several objective-functions, with linear constraints. Starting from the idea of Rosen's algorithm for solving the problem of convex programming with linear constraints, and taking into account the solution concept from multidimensional programming, represented by a program which reaches "the best compromise", we are extending this method in the case of multidimensional programming. The concept of direction of minimization is introduced, and a necessary and sufficient condition is given for a s ∈ R n direction to be a direction of minimization, according to the values of a criteria ensemble in a given point. The algorithm is interactive, and the intervention of the decident is minimal. The two numerical examples presented at the end validate the algorithm. © 1999 Korean Society for Computational & Applied Mathematics and Korean SIGCOAM (Korea Information Processing Society).