A Newton-Type Globally Convergent Interior-Point Method to Solve Multi-Objective Optimization Problems
Year: 2024
Author: Jauny, Debdas Ghosh, Ashutosh Upadhayay
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 24–48
Abstract
This paper proposes an interior-point technique for detecting the nondominated points of multi-objective optimization problems using the direction-based cone method. Cone method decomposes the multi-objective optimization problems into a set of single-objective optimization problems. For this set of problems, parametric perturbed KKT conditions are derived. Subsequently, an interior point technique is developed to solve the parametric perturbed KKT conditions. A differentiable merit function is also proposed whose stationary point satisfies the KKT conditions. Under some mild assumptions, the proposed algorithm is shown to be globally convergent. Numerical results of unconstrained and constrained multi-objective optimization test problems are presented. Also, three performance metrics (modified generational distance, hypervolume, inverted generational distance) are used on some test problems to investigate the efficiency of the proposed algorithm. We also compare the results of the proposed algorithm with the results of some other existing popular methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2204-m2021-0241
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 24–48
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Cone method Interior point method Merit function Newton method Global convergence.