Solution Approaches for Multiobjective Convex Quadratic and Nonlinear Optimization Problems

Abstract

In this thesis three solution approaches for multiobjective nonlinear optimization problems are discussed. First, a class of multiobjective descent algorithms is introduced that can be understood as generalizations of descent algorithms known for the singleobjective case. Several variants are investigated and compared with the weighted sum method. Furthermore, multiobjective convex quadratic optimization problems with linear constraints are discussed in the second part. Using the KKT conditions a parametric linear complementarity problem is derived which leads to the definition of efficient complementary bases and the decomposition of the parameter space of the weighted sum method. Properties of the associated cells are discussed and a pivoting algorithm is developed. Additionally, generalizations and special cases for multiobjective convex quadratic optimization problems are discussed and an application to multiobjective location theory is outlined. In the final section, a scheme for the approximation of the efficient solutions and the weight space decomposition of multiobjective convex optimization problems is introduced and analyzed.