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

Gabriele Eichfelder(gabriele.eichfelder***at***tu-ilmenau.de)
Leo Warnow(leo.warnow***at***tu-ilmenau.de)

Abstract: A central requirement for solving optimization problems numerically with the help of computer algorithms is the verification of the optimality of a found solution. A frequently used approach to meet this requirement 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 KKT conditions, can easily be computed, and moreover 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, which we also illustrate numerically for some common test problems.

Keywords: Multiobjective Optimization, KKT Approximation, Proximity Measure

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Global Optimization (Theory )

Citation:

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Entry Submitted: 12/17/2019
Entry Accepted: 12/17/2019
Entry Last Modified: 12/17/2019

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