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科学研究
报告题目:

A block Lanczos method for large-scale quadratic minimization problems with orthogonality constraints

报告人:

吴钢 教授(中国矿业大学)

报告时间:

报告地点:

老外楼信息与计算科学系报告厅

报告摘要:

Quadratic minimization problems with orthogonality constraints (QMPO) play an important role in many applications of science and engineering. However, some existing methods may suffer from low accuracy or heavy workload for large-scale QMPO. Krylov subspace methods are popular for large-scale optimization problems. In this work, we propose a block Lanczos method for solving the large-scale QMPO. In the proposed method, the original problem is projected into a small-sized one, and the Riemannian Trust-Region method is employed to solve the reduced QMPO. Convergence results on the optimal solution, the optimal objective function value, the multiplier and the KKT error are established. Moreover, we give the convergence speed of the approximate solution, and show that if the block Lanczos process terminates, then an exact KKT solution is derived. Numerical experiments illustrate the numerical behavior of the proposed algorithm, and demonstrate that it is more powerful than many state-of-the-art algorithms for large-scale QMPO.