Convergence analysis of a proximal point algorithm for minimizing differences of functions

DOI10.1080/02331934.2016.1253694zbMath1364.90266arXiv1504.08079OpenAlexW3103245321MaRDI QIDQ2977635

Nguyen Mau Nam, Nguyen Thai An

Publication date: 18 April 2017

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.08079

zbMATH Keywords

difference of convex functionsproximal point algorithmDC programmingKurdyka-Łojasiewicz inequality

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Interior-point methods (90C51)

Related Items (16)

Solving a continuous multifacility location problem by DC algorithms ⋮ Convergence guarantees for a class of non-convex and non-smooth optimization problems ⋮ Separating variables to accelerate non-convex regularized optimization ⋮ A New Boosted Proximal Point Algorithm for Minimizing Nonsmooth DC Functions ⋮ A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems ⋮ On a solution method in indefinite quadratic programming under linear constraints ⋮ Approximate versions of proximal iteratively reweighted algorithms including an extended IP-ICMM for signal and image processing problems ⋮ DC programming and DCA: thirty years of developments ⋮ A bundle method for nonsmooth DC programming with application to chance-constrained problems ⋮ On Algorithms for Difference of Monotone Operators ⋮ On Algorithms for Difference of Monotone Operators ⋮ The Boosted Difference of Convex Functions Algorithm for Nonsmooth Functions ⋮ Sequence Convergence of Inexact Nonconvex and Nonsmooth Algorithms with More Realistic Assumptions ⋮ A forward-backward algorithm for the DC programming in Hilbert spaces ⋮ A general double-proximal gradient algorithm for d.c. programming ⋮ Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems

Cites Work

• Unnamed Item
• Proximal alternating linearized minimization for nonconvex and nonsmooth problems
• A proximal point algorithm for DC functions on Hadamard manifolds
• On the convergence of the proximal algorithm for nonsmooth functions involving analytic features
• A proximal method with separable Bregman distances for quasiconvex minimization over the nonnegative orthant
• The DC (Difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems
• Convergence of Pham Dinh-Le Thi's algorithm for the trust-region subproblem
• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
• DC programming: overview.
• Majorization-Minimization Procedures and Convergence of SQP Methods for Semi-Algebraic and Tame Programs
• On difference convexity of locally Lipschitz functions
• Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality
• Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming
• Clarke Subgradients of Stratifiable Functions
• One step from DC optimization to DC mixed variational inequalities
• Monotone Operators and the Proximal Point Algorithm
• Variational Analysis
• A D.C. Optimization Algorithm for Solving the Trust-Region Subproblem
• Variational Analysis and Generalized Differentiation I
• Proximal point method for a special class of nonconvex functions on Hadamard manifolds
• The Łojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems
• Convex analysis and monotone operator theory in Hilbert spaces

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