On <em>q</em>-steepest descent method for unconstrained multiobjective optimization problems

Kin Keung Lai; Shashi Kant Mishra; Geetanjali Panda; Md Abu Talhamainuddin Ansary; Bhagwat Ram; Kin Keung Lai; Shashi Kant Mishra; Geetanjali Panda; Md Abu Talhamainuddin Ansary; Bhagwat Ram

doi:10.3934/math.2020354

AIMS Mathematics

2020, Volume 5, Issue 6: 5521-5540. doi: 10.3934/math.2020354

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Research article

On q-steepest descent method for unconstrained multiobjective optimization problems

1.
College of Economics, Shenzhen University, Shenzhen 518060, China
2.
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
3.
Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India
4.
Department of Economic Sciences, Indian Institute of Technology Kanpur, Kanpur 208016 India
5.
DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi 221005, India

Received: 28 April 2020 Accepted: 22 June 2020 Published: 28 June 2020
MSC : 90C29, 05A30, 34M60, 58E17, 90C53, 11Y16

The q-gradient is the generalization of the gradient based on the q-derivative. The q-version of the steepest descent method for unconstrained multiobjective optimization problems is constructed and recovered to the classical one as q equals 1. In this method, the search process moves step by step from global at the beginning to particularly neighborhood at last. This method does not depend upon a starting point. The proposed algorithm for finding critical points is verified in the numerical examples.
- multiobjective,
- q-calculus,
- steepest descent,
- pareto optimality,
- critical point,
- algorithms
Citation: Kin Keung Lai, Shashi Kant Mishra, Geetanjali Panda, Md Abu Talhamainuddin Ansary, Bhagwat Ram. On q-steepest descent method for unconstrained multiobjective optimization problems[J]. AIMS Mathematics, 2020, 5(6): 5521-5540. doi: 10.3934/math.2020354

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Abstract

The q-gradient is the generalization of the gradient based on the q-derivative. The q-version of the steepest descent method for unconstrained multiobjective optimization problems is constructed and recovered to the classical one as q equals 1. In this method, the search process moves step by step from global at the beginning to particularly neighborhood at last. This method does not depend upon a starting point. The proposed algorithm for finding critical points is verified in the numerical examples.

References

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