Speaker： Dr. Rujun Jiang

                         Fudan University

Title:    Novel reformulations and efficient algorithm for the generalized trust region subproblem

       Time：09 Dec 2019, 16:00

Location：实验楼105

Abstract:    We present a new solution framework to solve the generalized trust region subproblem (GTRS) of minimizing a quadratic objective over a quadratic constraint. More specifically, we derive a convex quadratic reformulation (CQR) via minimizing a linear objective over two convex quadratic constraints for the GTRS. We show that an optimal solution of the GTRS can be recovered from an optimal solution of the CQR. We further prove that this CQR is equivalent to minimizing the maximum of the two convex quadratic functions derived from the CQR for the case under investigation. Although the latter minimax problem is nonsmooth, it is well structured and convex. We thus develop two steepest descent algorithms corresponding to two different line search rules. We prove global sublinear convergence rates for both algorithms. We also obtain a local linear convergence rate of the first algorithm by estimating the Kurdyka– Lojasiewicz exponent at any optimal solution under mild conditions. We finally demonstrate the efficiency of our algorithms with numerical experiments

 Speaker  Introduction：江如俊，复旦大学大数据学院青年副研究员。2012年获得中国科学技术大学学士学位，2016年获得香港中文大学博士学位并留校继续从事博士后研究，2017年加入复旦大学。研究方向主要包括大规模优化算法和理论分析，二次规划，混合整数规划及其在运筹学、机器学习和信号处理领域的应用。在运筹优化杂志《Mathematical Programming》，《SIAM Journal on Optimization》，《INFORMS Journal on Computing》,《European Journal of Operational Research》等发表多篇论文。现为多个国际运筹优化杂志匿名审稿人及美国数学学会旗下Mathematical Reviews的评论员。

 联系人：黄文副教授