A family of inexact SQA methods for non-smooth convex minimization with provable convergence guarantees based on the Luo-Tseng error bound property
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Publication:1739040
DOI10.1007/s10107-018-1280-6zbMath1412.49061arXiv1605.07522OpenAlexW2964154161WikidataQ129905968 ScholiaQ129905968MaRDI QIDQ1739040
Zirui Zhou, Man-Chung Yue, Anthony Man-Cho So
Publication date: 24 April 2019
Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1605.07522
error boundsuperlinear convergenceproximal Newton methodconvex composite minimizationsequential quadratic approximation (SQA)
Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Methods of successive quadratic programming type (90C55)
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Cites Work
- A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
- An inexact successive quadratic approximation method for L-1 regularized optimization
- Practical inexact proximal quasi-Newton method with global complexity analysis
- An LP-Newton method: nonsmooth equations, KKT systems, and nonisolated solutions
- On the linear convergence of a proximal gradient method for a class of nonsmooth convex minimization problems
- A coordinate gradient descent method for \(\ell_{1}\)-regularized convex minimization
- Approximation accuracy, gradient methods, and error bound for structured convex optimization
- A coordinate gradient descent method for nonsmooth separable minimization
- Error bounds and convergence analysis of feasible descent methods: A general approach
- Error bounds in mathematical programming
- Local behavior of an iterative framework for generalized equations with nonisolated solutions
- Introductory lectures on convex optimization. A basic course.
- A unified approach to error bounds for structured convex optimization problems
- Calculus of the exponent of Kurdyka-Łojasiewicz inequality and its applications to linear convergence of first-order methods
- Regularized Newton methods for convex minimization problems with singular solutions
- Quadratic optimization with orthogonality constraint: explicit Łojasiewicz exponent and linear convergence of retraction-based line-search and stochastic variance-reduced gradient methods
- Adaptive restart for accelerated gradient schemes
- A family of Newton methods for nonsmooth constrained systems with nonisolated solutions
- Pathwise coordinate optimization
- A Globally Convergent LP-Newton Method
- Proximal Newton-Type Methods for Minimizing Composite Functions
- Linear Convergence of Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems
- A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix
- Implicit Functions and Solution Mappings
- On the Linear Convergence of Descent Methods for Convex Essentially Smooth Minimization
- Error Bound and Convergence Analysis of Matrix Splitting Algorithms for the Affine Variational Inequality Problem
- Sparse Reconstruction by Separable Approximation
- Finite-Dimensional Variational Inequalities and Complementarity Problems
- Signal Recovery by Proximal Forward-Backward Splitting
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