題 目：A globally convergent method for solving a quartic generalized Markowitz portfolio problem
主講人：王群博士
時(shí) 間：2023年5月11日（周四）13：30-14：30
地 點(diǎn)：6號學(xué)院樓500會(huì)議室
主辦單位：新葡萄8883官網(wǎng)AMG 浙江省2011 “數(shù)據(jù)科學(xué)與大數(shù)據(jù)分析協(xié)同創(chuàng)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.
主講人簡介：
王群，香港理工大學(xué)應(yīng)用數(shù)學(xué)博士，研究方向是最優(yōu)化、張量計(jì)算。主持過一項(xiàng)國家自然科學(xué)基金青年科學(xué)基金項(xiàng)目（2019），近幾年已發(fā)表SCI等學(xué)術(shù)論文十余篇。
歡迎各位老師和同學(xué)踴躍參加！
