Quadratic Growth Conditions for Convex Matrix Optimization Problems Associated with Spectral Functions
From MaRDI portal
Publication:4588864
DOI10.1137/17M1116325zbMath1376.65094arXiv1702.03262MaRDI QIDQ4588864
Xinyuan Zhao, Chao Ding, Ying Cui
Publication date: 3 November 2017
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1702.03262
convex programmingnumerical experimentspectral functionsaugmented Lagrangian functionmatrix optimizationmetric subregularityfast convergence ratesquadratic growth conditionsMarkov chain problem
Numerical mathematical programming methods (65K05) Convex programming (90C25) Sensitivity, stability, parametric optimization (90C31) Numerical analysis or methods applied to Markov chains (65C40)
Related Items
Augmented Lagrangian methods for convex matrix optimization problems ⋮ Kurdyka-Łojasiewicz exponent via inf-projection ⋮ Quadratic growth conditions and uniqueness of optimal solution to Lasso ⋮ Strong Variational Sufficiency for Nonlinear Semidefinite Programming and Its Implications ⋮ Local convergence analysis of augmented Lagrangian method for nonlinear semidefinite programming ⋮ Critical Multipliers in Semidefinite Programming ⋮ Spectral Operators of Matrices: Semismoothness and Characterizations of the Generalized Jacobian ⋮ 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 ⋮ An Inexact Augmented Lagrangian Method for Second-Order Cone Programming with Applications ⋮ On Degenerate Doubly Nonnegative Projection Problems ⋮ Hölderian Error Bounds and Kurdyka-Łojasiewicz Inequality for the Trust Region Subproblem
Uses Software
Cites Work
- An LP-Newton method: nonsmooth equations, KKT systems, and nonisolated solutions
- SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints
- Approximation accuracy, gradient methods, and error bound for structured convex optimization
- Higher-order metric subregularity and its applications
- On metric and calmness qualification conditions in subdifferential calculus
- Error bounds: necessary and sufficient conditions
- Metric subregularity and the proximal point method
- A simple characterization of solutions sets of convex programs
- Characterization of the subdifferential of some matrix norms
- A dual algorithm for the solution of nonlinear variational problems via finite element approximation
- Error bounds and convergence analysis of feasible descent methods: A general approach
- On matrix approximation problems with Ky Fan \(k\) norms
- Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices
- Solution of monotone complementarity problems with locally Lipschitzian functions
- Local behavior of an iterative framework for generalized equations with nonisolated solutions
- Sensitivity analysis of generalized equations
- A unified approach to error bounds for structured convex optimization problems
- QSDPNAL: a two-phase augmented Lagrangian method for convex quadratic semidefinite programming
- Strong conical hull intersection property, bounded linear regularity, Jameson's property \((G)\), and error bounds in convex optimization
- Variational analysis of the Ky Fan \(k\)-norm
- Stability analysis for composite optimization problems and parametric variational systems
- An introduction to a class of matrix cone programming
- Exact matrix completion via convex optimization
- On Lipschitzian Properties of Implicit Multifunctions
- Solving Nuclear Norm Regularized and Semidefinite Matrix Least Squares Problems with Linear Equality Constraints
- A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
- First Order and Second Order Characterizations of Metric Subregularity and Calmness of Constraint Set Mappings
- Asymptotic Convergence Analysis of the Proximal Point Algorithm
- Implicit Functions and Solution Mappings
- Fastest Mixing Markov Chain on Graphs with Symmetries
- Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
- Some continuity properties of polyhedral multifunctions
- Monotone Operators and the Proximal Point Algorithm
- First Order Conditions for General Nonlinear Optimization
- Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
- The Chebyshev Polynomials of a Matrix
- GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems
- Variational Analysis
- Strong Semismoothness of Eigenvalues of Symmetric Matrices and Its Application to Inverse Eigenvalue Problems
- On Projection Algorithms for Solving Convex Feasibility Problems
- Derivatives of Spectral Functions
- Finite-Dimensional Variational Inequalities and Complementarity Problems
- Convex Analysis on the Hermitian Matrices
- Semidefinite Programming
- Hölder Metric Subregularity with Applications to Proximal Point Method
- Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Programming
- The Power of Convex Relaxation: Near-Optimal Matrix Completion
- On Directional Metric Subregularity and Second-Order Optimality Conditions for a Class of Nonsmooth Mathematical Programs
- The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications
- Metric subregularity of the convex subdifferential in Banach spaces
- Fastest Mixing Markov Chain on a Path
- Convex Analysis
- Semismooth Matrix-Valued Functions
- A semismooth Newton-CG based dual PPA for matrix spectral norm approximation problems
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item