AIMS Mathematics, 2020, 5(6): 5521-5540. doi: 10.3934/math.2020354

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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

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.
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