Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization / von Bennet Gebken. Paderborn, 2022
Inhalt
- Introduction
- Basics of multiobjective optimization
- Pareto optimality
- Necessary optimality conditions and the Pareto critical set
- Existing solution methods
- Box-continuation methods for smooth problems
- An efficient descent method for nonsmooth problems
- Theoretical descent direction
- The Goldstein epsilon-subdifferential
- Efficient computation of descent directions
- The algorithm
- Numerical experiments
- Hierarchical structure of Pareto critical sets
- Topological and geometrical properties of the Pareto critical set
- Classifying Pareto critical points via KKT multipliers
- Tangent cones and the uniqueness of KKT vectors
- The boundary of the Pareto critical set
- Decomposing an MOP into lower-dimensional subproblems
- Examples
- Extension to constrained MOPs
- Extension to the nonsmooth case
- Inferring objective vectors from Pareto critical data
- Linearity of the inverse problem and its solution via SVD
- Applications
- Generating MOPs with prescribed properties
- Inferring objectives of stochastic MOPs
- Generation of surrogate models
- Open problems of our approach
- Conclusion and outlook
- List of symbols
- Bibliography