On inexact generalized proximal methods with a weakened error tolerance criterion

DOI10.1080/02331930410001661217zbMath1068.65064OpenAlexW2024265476MaRDI QIDQ4656055

Rainer Tichatschke, Alexander Kaplan

Publication date: 8 March 2005

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331930410001661217

zbMATH Keywords

convergenceiterationmaximal monotone operatorBregman functionproximal point method

Mathematics Subject Classification ID

Convex programming (90C25) Numerical optimization and variational techniques (65K10) Programming in abstract spaces (90C48)

Related Items (17)

Interior proximal extragradient method for equilibrium problems ⋮ An inexact proximal method for quasiconvex minimization ⋮ An inexact algorithm with proximal distances for variational inequalities ⋮ Interior point methods for equilibrium problems ⋮ A new convergence analysis and perturbation resilience of some accelerated proximal forward–backward algorithms with errors ⋮ An inexact scalarization proximal point method for multiobjective quasiconvex minimization ⋮ An interior proximal method for a class of quasimonotone variational inequalities ⋮ An inexact proximal method with proximal distances for quasimonotone equilibrium problems ⋮ An interior proximal method in vector optimization ⋮ Re-examination of Bregman functions and new properties of their divergences ⋮ Pseudomonotone operators and the Bregman proximal point algorithm ⋮ Interior proximal method without the cutting plane property ⋮ Perturbation resilience of proximal gradient algorithm for composite objectives ⋮ Extended auxiliary problem principle using Bregman distances ⋮ Interior Proximal Methods for equilibrium programming: part II ⋮ An interior proximal point algorithm for nonlinear complementarity problems ⋮ Bregman-like functions and proximal methods for variational problems with nonlinear constraints

Cites Work

• Convergence analysis of non-quadratic proximal methods for variational inequalities in Hilbert spaces
• Approximate iterations in Bregman-function-based proximal algorithms
• A logarithmic-quadratic proximal method for variational inequalities
• Some properties of generalized proximal point methods for quadratic and linear programming
• An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions
• Rescaling and Stepsize Selection in Proximal Methods Using Separable Generalized Distances
• Monotone Operators and the Proximal Point Algorithm
• Convergence of Proximal-Like Algorithms
• A Generalized Proximal Point Algorithm for the Variational Inequality Problem in a Hilbert Space

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