A Strongly Convergent Proximal Point Method for Vector Optimization

Alfredo N. Iusem (), Jefferson G. Melo () and Ray G. Serra ()
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Alfredo N. Iusem: Instituto de Matemática Pura e Aplicada
Jefferson G. Melo: Universidade Federal de Goiás
Ray G. Serra: Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2021, vol. 190, issue 1, No 8, 183-200

Abstract: Abstract In this paper, we propose and analyze a variant of the proximal point method for obtaining weakly efficient solutions of convex vector optimization problems in real Hilbert spaces, with respect to a partial order induced by a closed, convex and pointed cone with nonempty interior. The proposed method is a hybrid scheme that combines proximal point type iterations and projections onto some special halfspaces in order to achieve the strong convergence to a weakly efficient solution. To the best of our knowledge, this is the first time that proximal point type method with strong convergence has been considered in the literature for solving vector/multiobjective optimization problems in infinite dimensional Hilbert spaces.

Keywords: Proximal method; Vector optimization; Projection methods; Strong convergence; 90C25; 90C29; 90C30; 49J52; 90C48 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01877-0

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