An Inexact Augmented Lagrangian Method for Second-Order Cone Programming with Applications

DOI10.1137/20M1374262zbMath1472.90084arXiv2010.08772MaRDI QIDQ5003212

Defeng Sun, Ling Liang, Kim-Chuan Toh

Publication date: 20 July 2021

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

Full work available at URL: https://arxiv.org/abs/2010.08772

zbMATH Keywords

augmented Lagrangian methodsecond-order cone programmingtrust-region subproblemquadratic growth conditionminimal enclosing ball problemsquare-root Lasso problem

Mathematics Subject Classification ID

Semidefinite programming (90C22) Convex programming (90C25) Large-scale problems in mathematical programming (90C06)

Uses Software

• SDPT3
• QSDPNAL

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solving semidefinite-quadratic-linear programs using SDPT3
• Convergence analysis of the augmented Lagrangian method for nonlinear second-order cone optimization problems
• On the coderivative of the projection operator onto the second-order cone
• A simple characterization of solutions sets of convex programs
• Applications of second-order cone programming
• Second-order cone programming
• On implementing a primal-dual interior-point method for conic quadratic optimization
• Polynomial convergence of primal-dual algorithms for the second-order cone program based on the MZ-family of directions
• QSDPNAL: a two-phase augmented Lagrangian method for convex quadratic semidefinite programming
• Efficient algorithms for the smallest enclosing ball problem
• Strong conical hull intersection property, bounded linear regularity, Jameson's property \((G)\), and error bounds in convex optimization
• Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems
• Interior point methods for second-order cone programming and OR applications
• Geometric measure theory.
• Extension of Karmarkar's algorithm onto convex quadratically constrained quadratic problems
• Second-order variational analysis in second-order cone programming
• Metric subregularity and/or calmness of the normal cone mapping to the \(p\)-order conic constraint system
• On the R-superlinear convergence of the KKT residuals generated by the augmented Lagrangian method for convex composite conic programming
• Derivative-free filter simulated annealing method for constrained continuous global optimization
• Perturbation analysis of second-order cone programming problems
• Smoothing Functions for Second-Order-Cone Complementarity Problems
• A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
• Square-root lasso: pivotal recovery of sparse signals via conic programming
• Asymptotic Convergence Analysis of the Proximal Point Algorithm
• Monotone Operators and the Proximal Point Algorithm
• Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
• A convergence analysis of the scaling-invariant primal-dual path-following algorithms for second-order cone programming
• Quadratic Growth Conditions for Convex Matrix Optimization Problems Associated with Spectral Functions
• Upper bound limit analysis using simplex strain elements and second-order cone programming
• A Combined Smoothing and Regularization Method for Monotone Second-Order Cone Complementarity Problems
• A Second-Order Cone Based Approach for Solving the Trust-Region Subproblem and Its Variants
• Second‐Order Cone Programming Relaxation of Sensor Network Localization
• Second-order Cone Programming Methods for Total Variation-Based Image Restoration
• Convex Analysis
• Semismooth Homeomorphisms and Strong Stability of Semidefinite and Lorentz Complementarity Problems
• Solving Second Order Cone Programming via a Reduced Augmented System Approach