An inexact scalarization proximal point method for multiobjective quasiconvex minimization

E. A. Papa Quiroz () and S. Cruzado ()
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E. A. Papa Quiroz: Privada del Norte University and Mayor de San Marcos National University
S. Cruzado: Mayor de San Marcos National University

Annals of Operations Research, 2022, vol. 316, issue 2, No 32, 1445-1470

Abstract: Abstract In this paper we present an inexact scalarization proximal point algorithm to solve unconstrained multiobjective minimization problems where the objective functions are quasiconvex and locally Lipschitz. Under some natural assumptions on the problem, we prove that the sequence generated by the algorithm is well defined and converges. Then providing two error criteria we obtain two versions of the algorithm and it is proved that each sequence converges to a Pareto–Clarke critical point of the problem; furthermore, it is also proved that assuming an extra condition, the convergence rate of one of these versions is linear when the regularization parameters are bounded and superlinear when these parameters converge to zero.

Keywords: Proximal point method; Quasiconvex functions; Multiobjective minimization; Pareto optimality; Clarke subdifferential; Global convergence; Convergence rate; 90C26; 90C48; 65K05; 58C20 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10479-020-03622-8

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