组合优化和二次优化的混合线性和半定规划

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1999-01-01 DOI:10.1080/10556789908805761

S. Benson, Yinyu Yeb, Xiong Zhang

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引用次数: 50

摘要

我们使用半定松弛来逼近线性、二次和布尔约束下的组合和二次优化问题。我们提出了一种对偶势约简算法，并展示了如何利用各种问题的稀疏结构。结合随机化和启发式方法，我们报告了近似图划分和二次问题的计算结果，维数为800到10,000。据我们所知，这一发现是这些近似算法在解决大规模问题时有效性的第一个计算证据。

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Mixed linear and semidefinite programming for combinatorial and quadratic optimization

We use the semidefinite relaxation to approximate combinatorial and quadratic optimization problems subject to linear, quadratic, as well as boolean constraints. We present a dual potential reduction algorithm and show how to exploit the sparse structure of various problems. Coupled with randomized and heuristic methods, we report computational results for approximating graph-partition and quadratic problems with dimensions 800 to 10,000. This finding, to the best of our knowledge, is the first computational evidence of the effectiveness of these approximation algorithms for solving large-scale problems.

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来源期刊

Optimization Methods & Software 工程技术-计算机：软件工程

CiteScore

4.50

自引率

0.00%

发文量

审稿时长

7 months

期刊介绍： Optimization Methods and Software publishes refereed papers on the latest developments in the theory and realization of optimization methods, with particular emphasis on the interface between software development and algorithm design. Topics include: Theory, implementation and performance evaluation of algorithms and computer codes for linear, nonlinear, discrete, stochastic optimization and optimal control. This includes in particular conic, semi-definite, mixed integer, network, non-smooth, multi-objective and global optimization by deterministic or nondeterministic algorithms. Algorithms and software for complementarity, variational inequalities and equilibrium problems, and also for solving inverse problems, systems of nonlinear equations and the numerical study of parameter dependent operators. Various aspects of efficient and user-friendly implementations: e.g. automatic differentiation, massively parallel optimization, distributed computing, on-line algorithms, error sensitivity and validity analysis, problem scaling, stopping criteria and symbolic numeric interfaces. Theoretical studies with clear potential for applications and successful applications of specially adapted optimization methods and software to fields like engineering, machine learning, data mining, economics, finance, biology, or medicine. These submissions should not consist solely of the straightforward use of standard optimization techniques.