An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems

In multicriteria optimization, several objective functions, conflicting with each other, have to be minimized simultaneously. We propose a new efficient method for approximating the solution set of a multiobjective programming problem, where the objective functions involved are arbitary convex functions and the set of feasible points is convex. The method is based on generating warm-start points for an efficient interior-point algorithm, while the approximation computed consists of a finite set of discrete points. Complexity results for the method proposed are derived. It turns out that the number of operations per point decreases when the number of points generated for the approximation increases.