Pathfollowing methods for nonlinear multiobjective optimization problems

Abstract

The paper deals with multiobjective nonlinear optimization problems with equality and inequality con- straints. In a corresponding dialogue procedure the decision maker has to determine in each step the aspira- tion and reservation level expressing his goals. This leads to a nonlinear optimization problem which can be solved by using a combination of pathfollowing methods and feasible descent direction methods (so- called jumps). The authors propose the application of a recently published pathfollowing method with jumps to multiobjective optimization problems, discuss its topological properties and present several computational results.

Keywords:

• multiobjective optimization
• one-parametric optimization problems
• pathfollowing methods with jumps
• genericity
• Jongen-Jonker-Twilt regularity
• modified standard embedding