In multicriteria optimization, several objective functions have to be minimized simultaneously. For this kind of problem, no single solution can adequately represent the whole set of optimal points. We propose a new efficient method for approximating the solution set of a convex quadratic multiobjective programming problem. The method is based on a warm-start interior point algorithm for which we derive complexity results, thereby extending previous results by Yildirim & Wright. Numerical results on bicriteria problems from power plant optimization and portfolio optimization show that the method is an order of magnitude faster than standard methods applied to the problems considered.
Ergebnisberichte Angewandte Mathematik. No. 211. Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany. January 2002.