A fresh variational-analysis look at the positive semidefinite matrices world
From MaRDI portal
Publication:438781
DOI10.1007/s10957-011-9980-6zbMath1254.90166OpenAlexW2152560558MaRDI QIDQ438781
Jean-Baptiste Hiriart-Urruty, Jérôme Malick
Publication date: 31 July 2012
Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10957-011-9980-6
Convex programming (90C25) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57)
Related Items
A Taylor expansion of the square root matrix function, Regularity properties of non-negative sparsity sets, A variational approach of the rank function, Some recent developments in Markov Chain Monte Carlo for cointegrated time series, Solving the Problem of Simultaneous Diagonalization of Complex Symmetric Matrices via Congruence, Mathematical programs with complementarity constraints in Banach spaces, Strong stationarity for optimization problems with complementarity constraints in absence of polyhedricity. With applications to optimization with semidefinite and second-order-cone complementarity constraints, Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models, Duality for Optimization Problems with Infinite Sums, Complementarity problems with respect to Loewnerian cones, Optimality Conditions in Semidefinite Programming
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Explicit Sensor Network Localization using Semidefinite Representations and Facial Reductions
- Handbook on semidefinite, conic and polynomial optimization
- On the similarity transformation between a matrix and its transpose
- Conjugate cone characterization of positive definite and semidefinite matrices
- Definiteness and semidefiniteness of quadratic forms revisited
- Smoothing technique and its applications in semidefinite optimization
- Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices
- Sensitivity analysis of all eigenvalues of a symmetric matrix
- Nonsmooth analysis of eigenvalues
- Convex analysis and nonlinear optimization. Theory and examples
- On the Riemannian geometry defined by self-concordant barriers and interior-point methods.
- A recipe for semidefinite relaxation for \((0,1)\)-quadratic programming
- The resolvent average for positive semidefinite matrices
- On the averaging of symmetric positive-definite tensors
- Series and parallel addition of matrices
- Products of positive definite matrices. III
- The role of symmetric matrices in the study of general matrices
- A Variational Approach to Copositive Matrices
- Potpourri of Conjectures and Open Questions in Nonlinear Analysis and Optimization
- Riemannian Metric and Geometric Mean for Positive Semidefinite Matrices of Fixed Rank
- A new series of conjectures and open questions in optimization and matrix analysis
- An Invitation to Tame Optimization
- The Factorization of a Square Matrix Into Two Symmetric Matrices
- On Weakly Positive Matrices
- Linear Matrix Inequalities in System and Control Theory
- Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
- A Dual Approach to Semidefinite Least-Squares Problems
- Some Applications of the Cartan-Kähler Theorem to Economic Theory
- Alternating Projections on Manifolds
- The Łojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems
- A Direct Formulation for Sparse PCA Using Semidefinite Programming
- Handbook of semidefinite programming. Theory, algorithms, and applications
- Matrix theory. Basic results and techniques