1月5日 Fengmin Xu副教授学术报告

发布时间:2014-12-29

题 目：On Cardinality Constrained Optimization: Some Models and Algorithms

报告人：Xu Fengmin, Associate Professor
（School of Mathematics and Statistics, Xi’an Jiaotong University）

时 间： 1月5日（周一） 下午4：00-5：00

地 点：旧数学楼104室

报告摘要：
    Cardinality constrained optimization have attracted great deal of attentions in machine learning and financial engineering, which is generally considered to be NP-hard. In this talk, we mainly consider three cardinality constrained optimization model in index replicating, and present corresponding efficient algorithms. Firstly, we introduce the cardinality constrained index tracking model and propose the nonmonotone projected gradient (NPG) algorithm. The accumulation point of the sequence generated by the NPG algorithm is a local minimizer under some suitable conditions. Secondly, considering the uncertainty of return in reality, we build a robust cardinality constrained index tracking model, which is proved to be a second order conic programming (SOCP) with cardinality constraints. We design a hybrid algorithm by solving a sequence of SOCP problems under the frame of evolutionary algorithm. Moreover, we establish a distributed robust enhanced index tracking model by adding the chance constraint. According to the distribution information, we also transform it into a SOCP with cardinality constraints. Finally, some numerical experiments with factual financial data are conducted to test the effectiveness of model and the corresponding algorithms.

Keywords: Cardinality constrained optimization, index tracking, robust optimization, chance constraint

报告人简介：
http://gr.xjtu.edu.cn/web/fengminxu

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