Nonsmooth optimization using Taylor-like models: error bounds, convergence, and termination criteria

DOI10.1007/s10107-019-01432-wzbMath1459.65083arXiv1610.03446OpenAlexW2977046017WikidataQ127217092 ScholiaQ127217092MaRDI QIDQ2220664

Dmitriy Drusvyatskiy, Alexander D. Ioffe, Adrian S. Lewis

Publication date: 25 January 2021

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.03446

zbMATH Keywords

nonsmooth optimizationerror estimationEkeland's principleKurdyka-Łojasiewicz inequalityTaylor-like model

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10)

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Uses Software

• GradSamp

Cites Work

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• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• Accelerated gradient methods for nonconvex nonlinear and stochastic programming
• An inexact successive quadratic approximation method for L-1 regularized optimization
• Gradient methods for minimizing composite functions
• Proximal alternating linearized minimization for nonconvex and nonsmooth problems
• Quadratic growth and critical point stability of semi-algebraic functions
• Transversality and alternating projections for nonconvex sets
• Accelerating the cubic regularization of Newton's method on convex problems
• On gradients of functions definable in o-minimal structures
• Error bounds and convergence analysis of feasible descent methods: A general approach
• Nonsmooth equations in optimization. Regularity, calculus, methods and applications
• From error bounds to the complexity of first-order descent methods for convex functions
• On the variational principle
• A Gauss-Newton method for convex composite optimization
• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
• Efficiency of minimizing compositions of convex functions and smooth maps
• Cubic regularization of Newton method and its global performance
• Curves of Descent
• On the Evaluation Complexity of Composite Function Minimization with Applications to Nonconvex Nonlinear Programming
• Convergence of an Inexact Algorithm for Composite Nonsmooth Optimization
• Clarke Subgradients of Stratifiable Functions
• Implicit Functions and Solution Mappings
• Characterizations of Łojasiewicz inequalities: Subgradient flows, talweg, convexity
• On the global convergence of trust region algorithms for unconstrained minimization
• On the superlinear convergence of a trust region algorithm for nonsmooth optimization
• Descent methods for composite nondifferentiable optimization problems
• A model algorithm for composite nondifferentiable optimization problems
• Proximal Subgradients, Marginal Values, and Augmented Lagrangians in Nonconvex Optimization
• Monotone Operators and the Proximal Point Algorithm
• Optimization of lipschitz continuous functions
• Upper-Lipschitz multifunctions and inverse subdifferentials
• Metric regularity and subdifferential calculus
• Stochastic Model-Based Minimization of Weakly Convex Functions
• Prox-regular functions in variational analysis
• Variational Analysis of Regular Mappings
• Solving (most) of a set of quadratic equalities: composite optimization for robust phase retrieval
• Second-order growth, tilt stability, and metric regularity of the subdifferential
• Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods
• Composite Optimization by Nonconvex Majorization-Minimization
• A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization
• Modified Gauss–Newton scheme with worst case guarantees for global performance

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