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Volume 5, Issue 6, 1 December 2021, Pages 929-938
Abstract. In this paper, we consider a projected gradient method for constrained multiobjective optimization problems. Under suitable assumptions, we show that the sequence generated by the method converges to a Pareto stationary point (or a weak Pareto optimal point) of the problem when the multiobjective function is quasiconvex (or pseudoconvex). Furthermore, in the case that the multiobjective function is convex, by using some approximate conditions that are imposed on the gradients of the objective functions and the search directions, we obtain the linear convergence result for this method.
How to Cite this Article:
Xiaopeng Zhao, Qiaoyue Sun, Liya Liu, Sun Young Cho, Convergence analysis of a projected gradient method for multiobjective optimization problems, J. Nonlinear Var. Anal. 5 (2021), 929-938.