报告主题：广义信赖域子问题的新表述和高效算法
报告人：江如俊 副研究员 (复旦大学大数据学院）
报告时间：2018年10月22日（周一）10:30
报告地点：校本部G507
邀请人：徐 姿
报告摘要：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 our 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 for both algorithms their global sublinear convergence rates. We also obtain a local linear convergence rate of the first algorithm by estimating the Kurdyka-{\L}ojasiewicz exponent at any optimal solution under mild conditions. We finally demonstrate the efficiency of our algorithms in our numerical experiments.
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