数学学科学术报告(罗和治 浙江工业大学)

发布者:项晓玲   发布时间:2019-01-04  浏览次数:13

报告人:罗和治(浙江工业大学经贸管理学院教授,中国运筹学会数学规划分会理事)

题    目:New Global Approaches to Non-convex Quadratic Programming

时    间:110日(星期四)下午3:00-4:00

地    点:21幢第三会议室

摘要:We consider a quadratic program with a few negative eigenvalues (denoted by QP-r-NE) subject to linear and convex quadratic constraints that covers a broad range of applications and is known to be NP-hard even with one negative eigenvalue (r=1, denoted by QP1NE). In this paper, we first introduce a new global algorithm (called ADMBB), which integrates several simple effective optimization techniques such as alternative direction method (ADM), convex relaxation, initialization and branch-and-bound, to find a globally optimal solution to the underlying QP within a pre-specified epsilon-tolerance. We establish the global convergence of the algorithm and estimate its complexity. Second, we combine ADM, convex relaxation and line search technique to develop a global search algorithm (GSA) for QP1NE that can locate an optimal solution to QP1NE within epsilon-tolerance. We establish a worst-case complexity of the GSA. Preliminary numerical results demonstrate that the ADMBB algorithm can effectively find a global optimal solution to large-scale QP-r-NE instances when r<=10, and the GSA outperforms the ADMBB for most of the tested QP1NE instances.

个人简介:

罗和治,博士、博士后,浙江工业大学经贸管理学院教授,中国运筹学会数学规划分会理事。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期刊SIAM Journal on OptimizationMathematical Programming ComputationINFORMS Journal on ComputingComputational Optimization and ApplicationsJournal of Global Optimization等上发表SCI 论文20 余篇,出版专著1 部。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面上项目3项。入选浙江省“新世纪151人才工程”第二层次培养人员(2012)和浙江工业大学第三批青年学术带头人(2009)。曾获中国运筹学会青年科技奖提名奖(2010),复旦大学优秀博士后(2011),浙江省自然科学学术奖三等奖(2012)和浙江省高等学校科研成果奖二等奖(20092011)。曾多次学术访问美国伊利诺伊大学香槟分校、美国休斯顿大学、香港中文大学和香港城市大学。

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