应用数学进展  >> Vol. 5 No. 1 (February 2016)

随机对称不确定集下的线性互补问题
Linear Complementarity Problems under a Random Symmetric Uncertainty

DOI: 10.12677/AAM.2016.51001, PDF, HTML, XML, 下载: 1,746  浏览: 3,835  国家自然科学基金支持

作者: 吴丹:河南科技大学,数学与统计学院,河南 洛阳;韩继业:中国科学院应用数学研究所,北京

关键词: 不确定线性互补问题鲁棒解随机对称不确定集Uncertain Linear Complementarity Problems Robust Solution A Random Symmetric Uncertainty

摘要: 本文引入不确定线性互补问题鲁棒解的概念。而且,我们证明:如果不确定二次规划问题的robust Counterpart,这一鲁棒优化问题的存在最优解 ,并且最优值为0,那么就是不确定线性互补问题的鲁棒解。我们讨论当不确定集为随机对称分布时,线性互补问题的求解。借助于概率论知识,给出 为almost reliable鲁棒解的充要条件。
Abstract: In this paper, we introduce the notion of robust solution of uncertain linear complementarity problems. We prove that, if robust counterpart to uncertain quadratic programming—a robust optimization problem, has a optimal solution , and the optimum value equals to zero, then is the robust solution of the uncertain linear complementarity problem. By probability theory, we discuss linear complementarity problems under a random symmetric uncertainty, and obtain sufficient and necessary conditions of almost reliable robust solution.

文章引用: 吴丹, 韩继业. 随机对称不确定集下的线性互补问题[J]. 应用数学进展, 2016, 5(1): 1-7. http://dx.doi.org/10.12677/AAM.2016.51001

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