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Streaming Algorithms for Non-Submodular Maximizationon the Integer Lattice

Tsinghua Science and Technology 2023年第5期28卷 888-895页

作者： Jingjing Tan Yue Sun Yicheng Xu Juan Zou School of Mathematics and Information Science Weifang UniversityWeifang 261061China Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China Shenzhen Institute of Advanced Technology Chinese Academy of SciencesShenzhen 518055China School of Mathematical Sciences Qufu Normal UniversityQufu 273165China

Many practical problems emphasize the importance of not only knowing whether an element is selectedbut also deciding to what extent it is selected,which imposes a challenge on submodule optimization.In this study,we consider the monotone,nondecreasing,and non-submodular maximization on the integer lattice with a cardinalityconstraint.We first design a two-pass streaming algorithm by refining the estimation interval of the optimal value.Foreach element,the algorithm not only decides whether to save the element but also gives the number of reservations.Then,we introduce the binary search as a subroutine to reduce the time complexity.Next,we obtain a one-passstreaming algorithm by dynamically updating the estimation interval of optimal value.Finally,we improve the memorycomplexity of this algorithm.

关键词： integer lattice non-submodular streaming algorithm cardinality constraint

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A comparative study of heuristic methods for cardinality constrained portfolio optimization

高置信计算(英文)

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高置信计算(英文) 2023年第1期3卷 23-30页

作者： Lei Fu Jun Li Shanwen Pu Bank of Jiangsu Nanjing 210001China School of Economics Fudan UniversityShanghai 200433China School of Information Management and Engineering Shanghai University of Finance and EconomicsShanghai 200433China

The cardinality constrained mean–variance(CCMV)portfolio selection model aims to identify a subset of the candidate assets such that the constructed portfolio has a guaranteed expected return and minimum variance.By formulating this model as the mixed-integer quadratic program(MIQP),the exact solution can be solved by a branch-and-bound algorithm.However,computational efficiency is the central issue in the time-sensitive portfolio investment due to its NP-hardness properties.To accelerate the solution speeds to CCMV portfolio optimization problems,we develop various heuristic methods based on techniques such as continuous relaxation,l1-norm approximation,integer optimization,and relaxation of semi-definite programming(SDP).We evaluate our heuristic methods by applying them to the US equity market dataset.The experimental results show that our SDP-based method is effective in terms of the computation time and the approximation ratio.Our SDP-based method performs even better than a commercial MIQP solver when the computational time is limited.In addition,several investment companies in China have adopted our methods,gaining good returns.This paper sheds light on the computation optimization for financial investments.

关键词： Acceleration Mean-variance portfolio optimization cardinality constraint Mixed-integer programming

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