A Linear Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization

Erik Alex Papa Quiroz (), Hellena Christina Fernandes Apolinário (), Kely Diana Villacorta () and Paulo Roberto Oliveira ()
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Erik Alex Papa Quiroz: Universidad Nacional Mayor de San Marcos and Universidad Privada del Norte
Hellena Christina Fernandes Apolinário: Federal University of Tocantins
Kely Diana Villacorta: Federal University of Paraíba
Paulo Roberto Oliveira: Federal University of Rio de Janeiro

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 3, No 12, 1028-1052

Abstract: Abstract In this paper, we propose a linear scalarization proximal point algorithm for solving lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and, using the condition that the proximal parameters are bounded, we prove the convergence of the sequence generated by the algorithm and, when the objective functions are continuous, we prove the convergence to a generalized critical point of the problem. Furthermore, for the continuously differentiable case we introduce an inexact algorithm, which converges to a Pareto critical point.

Keywords: Multiobjective minimization; Lower semicontinuous quasiconvex functions; Proximal point methods; Fejér convergence; Pareto–Clarke critical point; 49M37; 65K05; 65K10; 90C26; 90C29 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-019-01582-z

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