A Monotonic Optimization Approach for Solving Strictly Quasiconvex Multiobjective Programming Problems

In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective functions are nonlinear fractional. After the algorithm is te...

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Bibliographic Details
Published in:arXiv.org 2020-03
Main Authors: Tran, Ngoc Thang, Solanki, Vijender Kumar, Dao, Tuan Anh, Nguyen Thi Ngoc Anh, Pham, Hai V
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computational geometry
Convexity
Mathematical analysis
Mathematical programming
Multiple objective analysis
Nonlinear programming
Optimization
Software
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Summary:In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective functions are nonlinear fractional. After the algorithm is terminated, with any given tolerance, we obtain an approximation of the weakly efficient solution set, that contains the whole weakly efficient solution set of the problem. The algorithm is proved to be convergent and it is suitable to be implemented in parallel using standard convex programming tools. Some computational experiments are reported to show the accuracy and efficiency of the proposed algorithm.
ISSN:2331-8422
DOI:10.48550/arxiv.2003.07549