Spectral Operators of Matrices: Semismoothness and Characterizations of the Generalized Jacobian
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Publication:5217598
DOI10.1137/18M1222235zbMath1434.49007arXiv1810.09856OpenAlexW3008034264MaRDI QIDQ5217598
Kim-Chuan Toh, Defeng Sun, Chao Ding, Jie Sun
Publication date: 25 February 2020
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1810.09856
Numerical mathematical programming methods (65K05) Convex programming (90C25) Large-scale problems in mathematical programming (90C06) Nonlinear programming (90C30) Nonsmooth analysis (49J52) Fréchet and Gateaux differentiability in optimization (49J50)
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Cites Work
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- Spectral (isotropic) manifolds and their dimension
- A rank-corrected procedure for matrix completion with fixed basis coefficients
- An implementable proximal point algorithmic framework for nuclear norm minimization
- First order optimality conditions for mathematical programs with semidefinite cone complementarity constraints
- SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints
- New fractional error bounds for polynomial systems with applications to Hölderian stability in optimization and spectral theory of tensors
- Quadratic growth and critical point stability of semi-algebraic functions
- A B-differentiable equation-based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems
- Tame functions are semismooth
- The Colin de Verdière number and sphere representations of a graph
- On the rank of a matrix associated with a graph.
- A unified approach to error bounds for structured convex optimization problems
- The Euclidean distance degree of orthogonally invariant matrix varieties
- \(\ell _p\) regularized low-rank approximation via iterative reweighted singular value minimization
- QSDPNAL: a two-phase augmented Lagrangian method for convex quadratic semidefinite programming
- On concepts of directional differentiability
- Über monotone Matrixfunktionen
- Structured low rank approximation
- The Josephy-Newton method for semismooth generalized equations and semismooth SQP for optimization
- Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
- A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities
- A nonsmooth version of Newton's method
- On eigenvalues of matrices dependent on a parameter
- Spectral operators of matrices
- An introduction to a class of matrix cone programming
- Nonsmooth analysis of singular values. I: Theory
- Nonsmooth analysis of singular values. II: Applications
- On totally differentiable and smooth functions
- Exact matrix completion via convex optimization
- Twice Differentiable Spectral Functions
- Majorization-Minimization Procedures and Convergence of SQP Methods for Semi-Algebraic and Tame Programs
- Curves of Descent
- Hankel Matrix Rank Minimization with Applications to System Identification and Realization
- Orthogonal Invariance and Identifiability
- Penalty decomposition methods for rank minimization
- Robust principal component analysis?
- A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
- Rank-Sparsity Incoherence for Matrix Decomposition
- GMRES vs. Ideal GMRES
- Nonsmooth Equations: Motivation and Algorithms
- Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras
- Newton's Method for B-Differentiable Equations
- Semidefinite optimization
- Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
- Constraint Nondegeneracy, Strong Regularity, and Nonsingularity in Semidefinite Programming
- An Invitation to Tame Optimization
- Optimization and nonsmooth analysis
- Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity
- Convex spectral functions
- On generalized matrix functions
- Semismooth and Semiconvex Functions in Constrained Optimization
- On the Shannon capacity of a graph
- The Chebyshev Polynomials of a Matrix
- GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems
- Smooth Interpolation, Holder Continuity, and the Takagi-van der Waerden Function
- Strong Semismoothness of Eigenvalues of Symmetric Matrices and Its Application to Inverse Eigenvalue Problems
- Qualification Conditions in Semialgebraic Programming
- On Efficiently Solving the Subproblems of a Level-Set Method for Fused Lasso Problems
- Quadratic Growth Conditions for Convex Matrix Optimization Problems Associated with Spectral Functions
- A Highly Efficient Semismooth Newton Augmented Lagrangian Method for Solving Lasso Problems
- Variational analysis of spectral functions simplified
- A Multigrid Semismooth Newton Method for Semilinear Contact Problems
- Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations
- Derivatives of Spectral Functions
- Finite-Dimensional Variational Inequalities and Complementarity Problems
- Convex Analysis on the Hermitian Matrices
- Second-Order Subdifferential Calculus with Applications to Tilt Stability in Optimization
- Full Stability in Finite-Dimensional Optimization
- A Superlinearly Convergent Smoothing Newton Continuation Algorithm for Variational Inequalities over Definable Sets
- A Formula for the Fréchet Derivative of a Generalized Matrix Function
- The Power of Convex Relaxation: Near-Optimal Matrix Completion
- The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications
- Functions of Matrices
- Convex Analysis
- Semismooth Matrix-Valued Functions
- Semismooth Homeomorphisms and Strong Stability of Semidefinite and Lorentz Complementarity Problems
- An exact penalty method for semidefinite-box-constrained low-rank matrix optimization problems
- Second-order directional derivatives of all eigenvalues of a symmetric matrix
- A semismooth Newton-CG based dual PPA for matrix spectral norm approximation problems