On q-steepest descent method for unconstrained multiobjective optimization problems

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. Keywords: multiobjective; q-calculus; steepest descent; pareto optimality; critical point; algorithms Mathematics Subject Classification: 90C29, 05A30, 34M60, 58E17, 90C53, 11Y16