题  目：A globally convergent method for solving a quartic generalized Markowitz portfolio problem

主讲人：王群博士

时  间：2023年5月11日（周四）13：30-14：30

地  点：6号学院楼500会议室

主办单位：yh86银河国际 浙江省2011 “数据科学与大数据分析协同创新中心”

摘要：

In this paper, a generalized Markowitz model, which is a convex kurtosis minimization under mean and variance constraints, is proposed. It has a close relationship to the classical Markowitz model. The corresponding optimization problem is a convex quartic polynomial minimization problem with linear and quadratic constraints, which differs from the non-convex polynomial optimization models in the literature. A numerical method with an alternating minimization framework is proposed to solve this quartic optimization problem to a global minimizer, whose global convergence is established under a mild assumption. With a careful separation of the nonlinear constraints in the alternating iterations, two subproblems are solved respectively by accelerated proximal gradient method and semidefinite relaxation method efficiently. Moreover, it is shown that the semidefintie relaxation is tight in this situation without any further assumption. A real data from eight stock indices and some synthetic data are tested for the feasibility of this model and the proposed algorithm, whose performance is quite promising.

主讲人简介：

王群，香港理工大学应用数学博士，研究方向是最优化、张量计算。主持过一项国家自然科学基金青年科学基金项目（2019），近几年已发表SCI等学术论文十余篇。

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