一、报告题目：An Efficient Global Algorithm for Worst-case Linear Optimization under Uncertainties Based on Nonlinear Semi-definite Relaxation

二、报告人：罗和治教授-浙江理工大学

三、报告时间：2022年4月14日星期四下午15:00

四、报告平台：腾讯会议

  会议ID：523 179 301

五、摘要：

The worst-case linear optimization (WCLO) with uncertainties in the right-hand-side of the constraints often arises from numerous applications such as systemic risk estimate in finance and stochastic optimization, which is known to be NP-hard. In this paper, we investigate the efficient global algorithm for WCLO based on its nonlinear semi-definite relaxation (SDR). We first derive an enhanced nonlinear SDR for WCLO via secant cuts and RLT approaches. A secant search algorithm is then proposed to solve the nonlinear SDR and its global convergence is established. Second, we propose a new global algorithm for WCLO, which integrates the nonlinear SDR with successive convex optimization method, initialization and branch-and-bound, to find a globally optimal solution to the underlying WCLO within a pre-specified $\epsilon$-tolerance. We establish the global convergence of the algorithm and estimate its complexity. Preliminary numerical results demonstrate that the proposed algorithm can effectively find a globally optimal solution to the WCLO instances.

六、报告人简介：

罗和治，博士，教授，浙江理工大学特聘教授，中国运筹学会理事，中国运筹学会数学优化分会理事，浙江省“151人才工程”第二层次人员。2007年3月获上海大学运筹学专业博士学位。曾多次访问美国UIUC和休斯顿大学、香港中文大学以及香港城市大学。研究方向为全局优化算法及其在金融和通信工程中的应用。已在国际运筹优化期刊SIAM Journal on Optimization、Mathematical Programming Computation、INFORMS Journal on Computing、Computational Optimization and Applications、Journal of Global Optimization、Journal of Optimization Theory and Applications等上发表SCI论文30余篇。主持了国家自然科学基金面上项目3项，中国博士后科学基金特别资助项目和面上项目各1项，浙江省自然科学基金重点项目1项、面上项目3项。曾获中国运筹学会青年科技奖提名奖、浙江省自然科学学术奖三等奖、浙江省高等学校科研成果奖二等奖。