An inexact spectral bundle method for convex quadratic semidefinite programming

作者：Lin, Huiling^*

来源：Computational Optimization and Applications, 2012, 53(1): 45-89.

DOI：10.1007/s10589-011-9443-x

• Semidefinite programming
• Nonsmooth optimization methods
• Inexact spectral bundle method
• Eigenvalue minimization problem
• Approximate subgradients

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.

• 出版日期2012-9
• 单位福建师范大学; 南阳理工学院