Convergence analysis of the Gauss-Newton method for convex inclusion and convex-composite optimization problems

DOI10.1016/j.jmaa.2011.11.062zbMath1239.65036OpenAlexW2064882318MaRDI QIDQ663722

Ng Kung-fu, Chong Li

Publication date: 27 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.11.062

zbMATH Keywords

Banach spaceGauss-Newton methodconvergence criterionweak-Robinson conditionmajorizing functionconvex processconvex-composite optimizationconvex inclusion problem

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Programming in abstract spaces (90C48)

Related Items

Extended Newton methods for conic inequalities: approximate solutions and the extended Smale \(\alpha\)-theory, Local convergence analysis of Newton's method for solving strongly regular generalized equations, Newton-type method for solving generalized inclusion, Convergence of the Gauss-Newton method for convex composite optimization problems under majorant condition on Riemannian manifolds, Inexact Newton method for non-linear functions with values in a cone, A robust semi-local convergence analysis of Newton's method for cone inclusion problems in Banach spaces under affine invariant majorant condition, Extended Newton-type method for nonlinear functions with values in a cone, Kantorovich's Theorem on Newton's Method for Solving Strongly Regular Generalized Equation, Quantitative Analysis for Perturbed Abstract Inequality Systems in Banach Spaces, On Convergence Rates of Linearized Proximal Algorithms for Convex Composite Optimization with Applications, On Newton's method for solving generalized equations, Error bounds for approximate solutions of abstract inequality systems and infinite systems of inequalities on Banach spaces

Uses Software

• NewtonLib

Cites Work

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• Optimality conditions for non-finite valued convex composite functions
• Subdifferentials of value functions and optimality conditions for DC and bilevel infinite and semi-infinite programs
• Complete characterizations of stable Farkas' lemma and cone-convex programming duality
• Robinson's implicit function theorem and its extensions
• Strong uniqueness and second order convergence in nonlinear discrete approximation
• A Gauss-Newton method for convex composite optimization
• Inequality systems and global optimization
• Extension of Newton's method to nonlinear functions with values in a cone
• Approximate Solutions of Analytic Inequality Systems
• Metric Regularity of Newton's Iteration
• On the Stability of the Feasible Set in Optimization Problems
• Variational Analysis in Semi-Infinite and Infinite Programming, II: Necessary Optimality Conditions
• Majorizing Functions and Convergence of the Gauss–Newton Method for Convex Composite Optimization
• Variational Analysis in Semi-Infinite and Infinite Programming, I: Stability of Linear Inequality Systems of Feasible Solutions
• Local properties of algorithms for minimizing nonsmooth composite functions
• Descent methods for composite nondifferentiable optimization problems
• First- and Second-Order Epi-Differentiability in Nonlinear Programming
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Optimal Error Bounds for the Newton–Kantorovich Theorem
• Monotone processes of convex and concave type
• Normed Convex Processes
• On convergence of the Gauss-Newton method for convex composite optimization.