分类: 数学 >> 计算数学 提交时间: 2022-08-25
摘要: In this paper, we study the linear complementarity problems on the monotone ex#2;tended second order cones. We demonstrate that the linear complementarity problem on the monotone extended second order cone can be converted into a mixed comple#2;mentarity problem on the non-negative orthant. We prove that any point satisfying the FB equation is a solution of the converted problem. We also show that the semi#2;smooth Newton method could be used to solve the converted problem, and we also provide a numerical example. Finally, we derive the explicit solution of a portfolio optimisation problem based on the monotone extended second order cone.
分类: 数学 >> 计算数学 提交时间: 2022-03-22
摘要: 0.618法是一维线搜索中针对一维单峰函数,应用最为广泛的一种方法。具有良好的收敛性,但其收敛性太慢,因此,本文基于函数在搜索区间端点和区间内任一点函数值的基础上,给出了一种普适性的线搜索加速策略,每步迭代都可以在较大程度上缩小函数值的不确定性区间。数值试验结果表明,其收敛速度较0.618法有所提高,尤其是当初始区间两端函数值相差较大或很大的情况下,本文改进算法可以很大程度上减小区间范围。