Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds

Erik Alex Papa Quiroz (), Nancy Baygorrea Cusihuallpa () and Nelson Maculan ()
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Erik Alex Papa Quiroz: Universidad Nacional Mayor de San Marcos and Universidad Privada del Norte
Nancy Baygorrea Cusihuallpa: Universidade Federal do Rio de Janeiro and Centro de Tecnologia Mineral-CETEM
Nelson Maculan: Universidade Federal do Rio de Janeiro

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 3, No 8, 879-898

Abstract: Abstract In this paper, we present two inexact scalarization proximal point methods to solve quasiconvex multiobjective minimization problems on Hadamard manifolds. Under standard assumptions on the problem, we prove that the two sequences generated by the algorithms converge to a Pareto critical point of the problem and, for the convex case, the sequences converge to a weak Pareto solution. Finally, we explore an application of the method to demand theory in economy, which can be dealt with using the proposed algorithm.

Keywords: Proximal point methods; Quasiconvex function; Hadamard manifolds; Multiobjective optimization; Pareto optimality; 49M37; 65K05; 65K10; 90C26; 90C29 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-020-01725-7

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