On the hierarchical structure of Pareto critical sets

Abstract

In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems considering subsets of the objective functions. If the Pareto critical set is completely described by its boundary (e.g. if we have more objective functions than dimensions in the parameter space), this can be used to solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set. This technique is especially useful for efficiently solving many-objective optimization problems by breaking them down into MOPs with a reduced number of objective functions.

References in corpus (3)

• Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis
• On the hierarchical structure of Pareto critical sets
• Hierarchical stratification of Pareto sets

Cited by in corpus (6)

• On the hierarchical structure of Pareto critical sets
• An efficient descent method for locally Lipschitz multiobjective optimization problems
• On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation
• Inverse multiobjective optimization: Inferring decision criteria from data
• Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models
• Topology of Pareto sets of strongly convex problems