A linear scalarization proximal point method for quasiconvex multiobjective minimization

DOI10.1007/s10957-019-01582-zzbMath1471.49022arXiv1510.00461OpenAlexW2976862921MaRDI QIDQ2278894

Hellena Christina Fernandes Apolinário, Kely Diana Villacorta, Paulo Roberto Oliveira, Erik Alex Papa Quiroz

Publication date: 11 December 2019

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.00461

zbMATH Keywords

proximal point methodsFejér convergencemultiobjective minimizationPareto-Clarke critical pointlower semicontinuous quasiconvex functions

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Multi-objective and goal programming (90C29) Numerical optimization and variational techniques (65K10) Numerical methods based on nonlinear programming (49M37)

Related Items

A nonmonotone gradient method for constrained multiobjective optimization problems ⋮ Convergence analysis of a projected gradient method for multiobjective optimization problems ⋮ Proximal algorithm with quasidistances for multiobjective quasiconvex minimization in Riemannian manifolds ⋮ On the convergence rate of a proximal point algorithm for vector function on Hadamard manifolds ⋮ A projected subgradient method for nondifferentiable quasiconvex multiobjective optimization problems ⋮ Convergence of a nonmonotone projected gradient method for nonconvex multiobjective optimization ⋮ Quasi-convex feasibility problems: subgradient methods and convergence rates ⋮ Convergence rates of subgradient methods for quasi-convex optimization problems ⋮ Linear convergence of a nonmonotone projected gradient method for multiobjective optimization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An inexact proximal method for quasiconvex minimization
• An interior proximal method in vector optimization
• Handbook of generalized convexity and generalized monotonicity
• A proximal point-type method for multicriteria optimization
• A scalarization proximal point method for quasiconvex multiobjective minimization
• Nonlinear multiobjective optimization
• Approximate efficiency and scalar stationarity in unbounded nonsmooth convex vector optimization problems
• Approximate proximal methods in vector optimization
• Clarke's Gradients and Epsilon-Subgradients in Banach Spaces
• An Existence Theorem in Vector Optimization
• ε-Subdifferential and ε-monotonicity
• Variational Analysis
• Proximal Methods in Vector Optimization
• Nonlinear Programming