Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization

DOI10.1137/20M1329937zbMath1468.90132arXiv2004.02345OpenAlexW3159126638MaRDI QIDQ4989930

Boris S. Mordukhovich, M. Ebrahim Sarabi

Publication date: 27 May 2021

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.02345

zbMATH Keywords

nonsmooth optimizationsuperlinear convergencegeneralized Newton methodprox-regular functionstilt-stable local minimizers

Mathematics Subject Classification ID

Sensitivity, stability, parametric optimization (90C31) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53)

Related Items

Estimates of generalized hessians for optimal value functions in mathematical programming, On the application of the SCD semismooth* Newton method to variational inequalities of the second kind, Generalized damped Newton algorithms in nonsmooth optimization via second-order subdifferentials, Globally convergent coderivative-based generalized Newton methods in nonsmooth optimization, Variational Convexity of Functions and Variational Sufficiency in Optimization, Aubin property for solution set in multi-objective programming, A Chain Rule for Strict Twice Epi-Differentiability and Its Applications, On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Erratum to ``Generalized Newton's method based on graphical derivatives
• On directional metric regularity, subregularity and optimality conditions for nonsmooth mathematical programs
• On the Newton method for set-valued maps
• On the Aubin property of a class of parameterized variational systems
• Local analysis of Newton-type methods for variational inequalities and nonlinear programming
• Nonsmooth equations in optimization. Regularity, calculus, methods and applications
• Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems
• A nonsmooth version of Newton's method
• Second-order characterizations of tilt stability with applications to nonlinear programming
• Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization
• Newton's Method for B-Differentiable Equations
• A Lagrangian finite generation technique for solving linear-quadratic problems in stochastic programming
• Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity
• Variational Analysis
• Tilt Stability of a Local Minimum
• Variational Analysis and Applications
• Characterization of Tilt Stability via Subgradient Graphical Derivative with Applications to Nonlinear Programming
• Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations
• A Globally and Superlinearly Convergent Algorithm for Nonsmooth Convex Minimization
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• Prox-regular functions in variational analysis
• Second-Order Subdifferential Calculus with Applications to Tilt Stability in Optimization
• Parabolic regularity in geometric variational analysis
• Twice Epi-Differentiability of Extended-Real-Valued Functions with Applications in Composite Optimization
• Newton-Type Methods for Optimization and Variational Problems
• Implicit Functions and Solution Mappings
• Semismooth Matrix-Valued Functions
• On a Semismooth* Newton Method for Solving Generalized Equations
• A further result on an implicit function theorem for locally Lipschitz functions