Extending Mehrotra and Gondzio higher order methods to mixed semidefinite-quadratic-linear programming

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1999-01-01 DOI:10.1080/10556789908805748

J. Haeberly, M. V. Nayakkankuppam, M. Overton

引用次数: 10

Abstract

We discuss extensions of Mehrotra's higher order corrections scheme and Gondzio's multiple centrality corrections scheme to mixed semidefinite-quadratic-linear programming (SQLP). These extensions have been included in a solver for SQLP written in C and based on LAPACK. The code implements a primal-dual path-following algorithm for solving SQLP problems based on the XZ + ZX search direction and Mehrotra's predictor-corrector method. We present benchmarks showing that the use of the higher order schemes yields substantial reductions in both the number of iterations and the running time of the algorithm, and also improves its robustness.

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将Mehrotra和gonzio高阶方法推广到混合半定二次线性规划

讨论了Mehrotra的高阶校正方案和gonzio的多重中心性校正方案在混合半定二次线性规划(SQLP)中的推广。这些扩展已经包含在用C编写的基于LAPACK的SQLP求解器中。该代码实现了一个基于XZ + ZX搜索方向和Mehrotra的预测校正方法的原始对偶路径跟踪算法，用于解决SQLP问题。我们提供的基准测试表明，使用高阶方案大大减少了迭代次数和算法的运行时间，并且还提高了其鲁棒性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.