基于正渐近核函数的特殊加权线性互补问题全牛顿步长内部点算法

IF 2 3区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Optimization and Engineering Pub Date : 2023-12-14 DOI:10.1007/s11081-023-09873-1

Mingwang Zhang, Dechun Zhu, Jiawei Zhong

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引用次数: 0

摘要

原对偶内点法是求解线性互补问题最有效的方法之一。作为线性互补问题的扩展，对加权线性互补问题的研究显得尤为必要。针对一类特殊加权线性互补问题，提出了一种新的全牛顿阶跃原对偶内点算法。在每次迭代中，通过正渐近核函数确定方法的搜索方向。对算法的迭代复杂度进行了分析，结果与目前已知的同类方法的复杂度界一致。最后，通过数值算例验证了算法的有效性。

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A full-Newton step interior-point algorithm for the special weighted linear complementarity problem based on positive-asymptotic kernel function

The primal-dual interior-point method is widely recognized as one of the most effective approaches for solving the linear complementarity problem. As an extension of the linear complementarity problem, the study of the weighted linear complementarity problem is more necessary. In this paper, a new full-Newton step primal-dual interior-point algorithm is proposed for the special weighted linear complementarity problem. At each iteration, the search directions of the method are determined via a positive-asymptotic kernel function. The iteration complexity of the algorithm is analyzed, and the result is the same as the currently best known complexity bound of the similar methods. Finally, the validity of the algorithm is verified by some numerical results.

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来源期刊

Optimization and Engineering 工程技术-工程：综合

CiteScore

4.80

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Optimization and Engineering is a multidisciplinary journal; its primary goal is to promote the application of optimization methods in the general area of engineering sciences. We expect submissions to OPTE not only to make a significant optimization contribution but also to impact a specific engineering application. Topics of Interest: -Optimization: All methods and algorithms of mathematical optimization, including blackbox and derivative-free optimization, continuous optimization, discrete optimization, global optimization, linear and conic optimization, multiobjective optimization, PDE-constrained optimization & control, and stochastic optimization. Numerical and implementation issues, optimization software, benchmarking, and case studies. -Engineering Sciences: Aerospace engineering, biomedical engineering, chemical & process engineering, civil, environmental, & architectural engineering, electrical engineering, financial engineering, geosciences, healthcare engineering, industrial & systems engineering, mechanical engineering & MDO, and robotics.