Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization of Hadamard Manifolds

Glaydston de C. Bento (), João Xavier Cruz Neto () and Lucas V. Meireles ()
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Glaydston de C. Bento: Universidade Federal de Goiás
João Xavier Cruz Neto: Universidade Federal do Piauí
Lucas V. Meireles: Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 1, No 2, 37-52

Abstract: Abstract A proximal point method for nonsmooth multiobjective optimization in the Riemannian context is proposed, and an optimality condition for multiobjective problems is introduced. This allowed replacing the classic approach, via “scalarization,” by a purely vectorial and considering the method without any assumption of convexity over the constraint sets that determine the vectorial improvement steps. The main convergence result ensures that each cluster point (if any) of any sequence generated by the method is a Pareto critical point. Moreover, when the problem is convex on a Hadamard manifold, full convergence of the method for a weak Pareto optimal is obtained.

Keywords: Multiobjective optimization; Hadamard manifold; Proximal method; 90C29; 90C30; 49M30 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10957-018-1330-5

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