一、报告题目：Effective algorithms for optimal portfolio selection with relative marginal risk constraints

二、报告人：罗和治 教授

三、报告时间：2025年6月29日(周一) 14:00-15:30

四、报告地点：闻理园A4-305

报告摘要：We consider in this paper an optimal portfolio selection with relative marginal risk control in the mean-variance framework, a challenge previously studied but not globally solved in the literature. Its optimization model is a non-convex program with a convex quadratic objective function and quadratic fractional constraints. We first reformulate the optimization model as a new non-convex quadratically constrained quadratic program (QCQP) that is known to be NP-hard. We then propose a successive convex optimization (SCO) algorithm to find a KKT point of this non-convex QCQP. Second,  we develop an effective global algorithm, which combines the SCO approach and  second-order cone programming relaxation within the branch-and-bound framework, to find a globally optimal solution to this non-convex QCQP within a pre-specified $\epsilon$-tolerance. We establish both the global convergence and the computational complexity of the proposed algorithm. Additionally, we report numerical experiments to demonstrate the effectiveness of the proposed algorithm in finding a globally optimal solution to medium and large-scale random instances.

报告人简介：罗和治，博士，浙江师范大学“双龙学者”特聘教授（A类）、博士生导师，浙江省“151人才工程”第二层次入选者。现任中国运筹学会理事，中国运筹学会数学规划分会常务理事。主要研究方向为全局最优化理论与算法及其在金融工程中的应用。已在国际运筹与优化权威期刊SIAM Journal on Optimization、Mathematical Programming Computation、Mathematical Finance、INFORMS Journal on Computing、Computational Optimization 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4 项，国家自然科学基金区域创新联合基金重点项目子课题1项，中国博士后科学基金特别资助项目1 项，浙江省自然科学基金重点项目1项和面上项目3项。曾获中国运筹学会青年科技奖提名奖（2010）、浙江省自然科学学术奖三等奖（2012）。

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