390013 UK VGSCO: Computational Methods in Multiobjective Optimization (2021W)

This lecture series gives an introduction to multiobjective optimization, i.e., to optimizing multiple objective functions at the same time. First, the basic optimality notions and the needed theoretical background will be given. Then, the main focus is on numerical methods for solving such types of problems. A widely used tool are scalarization approaches as, for instance, the well-known weighted sum method. We will examine such approaches and discuss their advantages and limits. Another topic will be descent methods, for which we examine optimality conditions as stationarity. The course continuous with direct methods for solving multiobjective optimization problems and with the examination of special classes as mixed-integer nonlinear problems or robustness concepts in case of uncertain multiobjective optimization. As multiobjective optimization is a special case of vector optimization, i.e., of optimizing a vector-valued objective function, and of set-optimization, i.e. of optimizing a set-valued objective function, we will also give outlooks to these more general problem classes.