An inexact spectral bundle method for convex quadratic semidefinite programming

Abstract

Abstract. 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 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 programming 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.

Accelerated bundle level methods with inexact oracle

“…然而, ABL 和 APL 算法均涉及求解两个子问题: 一个线性优化类似于 (1.7) 和一个二次优化 (1.8). [13][14][15][16][17][18][19] 和应用 [20][21][22][23][24][25] . 然而到目前为止, 所有这些工作都是针对于求 解非光滑函数的优化问题, 未涉及求解光滑问题和半光滑问题, 并且所使用的是非加速的 BL 类算法.…”

Modified alternating direction method of multipliers for convex quadratic semidefinite programming

“…Meanwhile, there are several methods available for solving some special case of (1), including the inexact interior-point methods [4,5,9,10], the alternating direction methods [7,22,30], the quasi-Newton method [11], the inexact semi-smooth Newton-CG method [21], inexact accelerated proximal gradient (IAPG) method [20] and other methods [8,24].…”

A Novel Approach for Solving Semidefinite Programs

“…Zhadan and Orlov [19] presented a dual interior point method for linear SDP problem. Lin [20] proposed an inexact spectral bundle method for convex quadratic SDP. Sun and Zhang [21] proposed a modified alternating direction method for solving convex quadratically constrained quadratic SDP, which requires much less computational effort per iteration than the second-order approaches.…”