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单调线性权互补问题的新全牛顿步可行内点算法

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提出求解单调线性权互补问题(WLCP)的全牛顿步可行内点算法.基于线性优化的连续可微函数,给出中心方程的新等价形式,接着运用牛顿法求解定义中心路径的等价方程组,从而得到单调WLCP的新搜索方向.沿该搜索方向使用全牛顿步,无需进行线搜索.通过适当选取参数,分析了全牛顿步的严格可行性,证得算法是二次收敛的且具有多项式时间迭代复杂度.最后数值实验结果表明算法有效.
A new full-Newton step feasible interior-point method for the monotone weighted linear complementarity problem
A full-Newton step feasible interior-point method was proposed to solve the monotone weighted linear comple-mentarity problem(WLCP).Based on continuously differentiable function for linear optimization,new equivalent form of the central equation was given.Then Newton's method was applied to the equivalent system of equations defining the central path,which leads to new search direction for the monotone WLCP.Full-Newton steps are used along this search direction,and hence no line search was required.By appropriately selecting parameters,the strict feasibility of the full-Newton step was analyzed.It was proved that the algorithm was quadratically convergent and has polynomial time iteration complexity.Some numerical re-sults showed that the algorithm was effective.

monotone weighted linear complementarity problemfull-Newton stepfeasible interior-point algorithmalgebra-ic equivalent transformation

迟晓妮、杨玉萍、刘三阳、柳乐

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桂林电子科技大学数学与计算科学学院,广西桂林 541004

桂林电子科技大学广西高校数据分析与计算重点实验室,广西桂林 541004

桂林电子科技大学广西应用数学中心,广西桂林 541004

西安电子科技大学数学与统计学院,陕西西安 710071

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单调线性权互补问题 全牛顿步 可行内点算法 代数等价变换

国家自然科学基金资助项目广西自然科学基金资助项目广西大学生创新训练计划资助项目冶金工业过程系统科学湖北省重点实验室(武汉科技大学)开放基金项目

123610642021GXNSFAA220034S202310595188Z202301

2024

南昌大学学报(理科版)
南昌大学

南昌大学学报(理科版)

CSTPCD
影响因子：0.418
ISSN：1006-0464
年,卷(期)：2024.48(3)