Proximity measures based on KKT points for constrained multi-objective optimization

Artikel

An important aspect of optimization algorithms, for instance evolutionary algorithms, are termination criteria that measure the proximity of the found solution to the optimal solution set. A frequently used approach is the numerical verification of necessary optimality conditions such as the Karush–Kuhn–Tucker (KKT) conditions. In this paper, we present a proximity measure which characterizes the violation of the KKT conditions. It can be computed easily and is continuous in every efficient solution. Hence, it can be used as an indicator for the proximity of a certain point to the set of efficient (Edgeworth-Pareto-minimal) solutions and is well suited for algorithmic use due to its continuity properties. This is especially useful within evolutionary algorithms for candidate selection and termination, which we also illustrate numerically for some test problems.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Journal of Global Optimization ; ISSN: 1573-2916 ; Volume: 80 ; Year: 2020 ; Issue: 1 ; Pages: 63-86 ; New York, NY: Springer US

Classification and Topics

• Classification: Mathematik ; Single Equation Models: Single Variables: Instrumental Variables (IV) Estimation ; Single Equation Models; Single Variables: Other ; Specific Distributions; Specific Statistics ; Econometric Modeling: Other
• Subject: Multiobjective optimization ; KKT approximation ; Proximity measure

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Eichfelder, Gabriele ; Warnow, Leo
• Event: Veröffentlichung
• (who): Springer US
• (where): New York, NY
• (when): 2020

Further information

• DOI: doi:10.1007/s10898-020-00971-3
• Last update: 10.03.2025, 11:42 AM CET