Globally convergent coderivative-based generalized Newton methods in nonsmooth optimization
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Publication:6126654
DOI10.1007/s10107-023-01980-2arXiv2109.02093OpenAlexW3197368557MaRDI QIDQ6126654
Vo Thanh Phat, Boris S. Mordukhovich, Dat Ba Tran, Pham Duy Khanh
Publication date: 9 April 2024
Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2109.02093
generalized Newton methodsglobal convergencenonsmooth optimizationvariational analysisconvex composite optimizationlasso problemslinear and superlinear convergence rates
Sensitivity, stability, parametric optimization (90C31) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53)
Cites Work
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- Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
- A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
- First order optimality conditions for mathematical programs with semidefinite cone complementarity constraints
- A simple formula for the second-order subdifferential of maximum functions
- On directional metric regularity, subregularity and optimality conditions for nonsmooth mathematical programs
- Characterizing convexity of a function by its Fréchet and limiting second-order subdifferentials
- On the Newton method for set-valued maps
- Generalized Newton's method based on graphical derivatives
- Lectures on convex optimization
- Generalized Hessian matrix and second-order optimality conditions for problems with \(C^{1,1}\) data
- Optimal control of the sweeping process over polyhedral controlled sets
- Generalized differentiation of piecewise linear functions in second-order variational analysis
- On \(M\)-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling.
- Coderivatives of normal cone mappings and Lipschitzian stability of parametric variational inequalities
- On the coderivative of the projection operator onto the second-order cone
- On the co-derivative of normal cone mappings to inequality systems
- A dual algorithm for the solution of nonlinear variational problems via finite element approximation
- Local analysis of Newton-type methods for variational inequalities and nonlinear programming
- Newton's method for a class of nonsmooth functions
- Nonsmooth equations in optimization. Regularity, calculus, methods and applications
- Regularized Newton methods for convex minimization problems with singular solutions
- Least angle regression. (With discussion)
- A globally convergent Newton method for convex \(SC^ 1\) minimization problems
- Minimization of \(SC^ 1\) functions and the Maratos effect
- Sparse regression with exact clustering
- Augmented Lagrangian method for second-order cone programs under second-order sufficiency
- Generalized differentiation of a class of normal cone operators
- Forward-backward quasi-Newton methods for nonsmooth optimization problems
- A nonsmooth version of Newton's method
- Coderivative calculations related to a parametric affine variational inequality. I: Basic calculations
- Second-order characterizations of tilt stability with applications to nonlinear programming
- Multiplier and gradient methods
- Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization
- Augmented Lagrangians and hidden convexity in sufficient conditions for local optimality
- A globally convergent proximal Newton-type method in nonsmooth convex optimization
- On Second-Order Subdifferentials and Their Applications
- Local Monotonicity and Full Stability for Parametric Variational Systems
- Characterizations of Full Stability in Constrained Optimization
- Proximal Splitting Methods in Signal Processing
- Proximal Newton-Type Methods for Minimizing Composite Functions
- Introduction to Nonlinear Optimization
- Second-Order Analysis of Polyhedral Systems in Finite and Infinite Dimensions with Applications to Robust Stability of Variational Inequalities
- Newton's Method for B-Differentiable Equations
- Complete Characterizations of Tilt Stability in Nonlinear Programming under Weakest Qualification Conditions
- Splitting Algorithms for the Sum of Two Nonlinear Operators
- Quasi-Newton Methods, Motivation and Theory
- Complete Characterization of Openness, Metric Regularity, and Lipschitzian Properties of Multifunctions
- Variational Analysis
- Tilt Stability of a Local Minimum
- The Primal-Dual Active Set Strategy as a Semismooth Newton Method
- Variational Analysis and Applications
- Characterization of Tilt Stability via Subgradient Graphical Derivative with Applications to Nonlinear Programming
- Forward-Backward Envelope for the Sum of Two Nonconvex Functions: Further Properties and Nonmonotone Linesearch Algorithms
- First-Order Methods in Optimization
- A Highly Efficient Semismooth Newton Augmented Lagrangian Method for Solving Lasso Problems
- Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations
- Convergence Properties of the Inexact Levenberg-Marquardt Method under Local Error Bound Conditions
- Characterizations of Strong Regularity for Variational Inequalities over Polyhedral Convex Sets
- Finite-Dimensional Variational Inequalities and Complementarity Problems
- Second-Order Subdifferential Calculus with Applications to Tilt Stability in Optimization
- Parabolic regularity in geometric variational analysis
- Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization
- Variational Analysis of Composite Models with Applications to Continuous Optimization
- Twice Epi-Differentiability of Extended-Real-Valued Functions with Applications in Composite Optimization
- Second-order growth, tilt stability, and metric regularity of the subdifferential
- Full Stability of Locally Optimal Solutions in Second-Order Cone Programs
- Tilt Stability, Uniform Quadratic Growth, and Strong Metric Regularity of the Subdifferential
- Newton-Type Methods for Optimization and Variational Problems
- Implicit Functions and Solution Mappings
- Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming
- On a Semismooth* Newton Method for Solving Generalized Equations
- Convex analysis and monotone operator theory in Hilbert spaces
- From Perspective Maps to Epigraphical Projections
- A Generalized Newton Method for Subgradient Systems
