Proximity control in bundle methods for convex
Mathematical Programming: Series A and B
The Euclidian Distance Matrix Completion Problem
SIAM Journal on Matrix Analysis and Applications
Sensitivity analysis of all eigenvalues of a symmetric matrix
Numerische Mathematik
Variable metric bundle methods: from conceptual to implementable forms
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
SIAM Journal on Scientific Computing
SIAM Journal on Optimization
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
On the Nesterov--Todd Direction in Semidefinite Programming
SIAM Journal on Optimization
SIAM Journal on Optimization
A Proximal Bundle Method Based on Approximate Subgradients
Computational Optimization and Applications
An inexact bundle method for solving large structured linear matrix inequalities
An inexact bundle method for solving large structured linear matrix inequalities
First-Order and Second-Order Conditions for Error Bounds
SIAM Journal on Optimization
Algorithm 845: EIGIFP: a MATLAB program for solving large symmetric generalized eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
Error Bounds for Eigenvalue and Semidefinite Matrix Inequality Systems
Mathematical Programming: Series A and B
A Proximal Bundle Method with Approximate Subgradient Linearizations
SIAM Journal on Optimization
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
A Bundle Method for a Class of Bilevel Nonsmooth Convex Minimization Problems
SIAM Journal on Optimization
An inexact primal–dual path following algorithm for convex quadratic SDP
Mathematical Programming: Series A and B
A bundle method for solving equilibrium problems
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
A bundle-filter method for nonsmooth convex constrained optimization
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
A Trust Region Spectral Bundle Method for Nonconvex Eigenvalue Optimization
SIAM Journal on Optimization
Mathematical Programming: Series A and B
Calibrating Least Squares Semidefinite Programming with Equality and Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
Correlation stress testing for value-at-risk: an unconstrained convex optimization approach
Computational Optimization and Applications
Optimization Methods & Software - The 2nd Veszprem Optimization Conference: Advanced Algorithms (VOCAL), 13-15 December 2006, Veszprem, Hungary
Bundle Methods for Regularized Risk Minimization
The Journal of Machine Learning Research
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We present an inexact spectral bundle method for solving convex quadratic semidefinite optimization problems. This method is a first-order method, hence requires much less computational cost in each iteration than second-order approaches such as interior-point methods. In each iteration of our method, we solve an eigenvalue minimization problem inexactly, and solve a small convex quadratic semidefinite program as a subproblem. We give a proof of the global convergence of this method using techniques from the analysis of the standard bundle method, and provide a global error bound under a Slater type condition for the problem in question. Numerical experiments with matrices of order up to 3000 are performed, and the computational results establish the effectiveness of this method.