In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex n...In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.展开更多
A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal proble...A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal problem via incorporating an auxiliary variable is constructed. A combined approach of logarithm barrier and quadratic penalty function is proposed to solve the problem. Based on Newton＇s method, the global convergence of interior point and line search algorithm is proven. Only a finite number of iterations is required to reach an approximate optimal solution. Numerical tests are given to show the effectiveness of the method.展开更多
In this paper we propose a class of new large-update primal-dual interior-point algorithms for P.（k） nonlinear complementarity problem （NCP）, which are based on a class of kernel functions investigated by Bai et a...In this paper we propose a class of new large-update primal-dual interior-point algorithms for P.（k） nonlinear complementarity problem （NCP）, which are based on a class of kernel functions investigated by Bai et al. in their recent work for linear optimization （LO）. The arguments for the algorithms are followed as Peng et al.＇s for P.（n） complementarity problem based on the self-regular functions [Peng, J., Roos, C., Terlaky, T.： Self-Regularity： A New Paradigm for Primal-Dual Interior- Point Algorithms, Princeton University Press, Princeton, 2002]. It is worth mentioning that since this class of kernel functions includes a class of non-self-regular functions as special case, so our algorithms are different from Peng et al.＇s and the corresponding analysis is simpler than theirs. The ultimate goal of the paper is to show that the algorithms based on these functions have favorable polynomial complexity.展开更多
大量工程应用问题可建模为结构化非线性规划,且这类问题的系数矩阵可分为稀疏型和稠密型两种类型.利用原始-对偶内点法(primal dual interior point method,PD-IPM),并结合分布式并行技术可高效求解此类问题.经典工程问题-机组组合(unit...大量工程应用问题可建模为结构化非线性规划,且这类问题的系数矩阵可分为稀疏型和稠密型两种类型.利用原始-对偶内点法(primal dual interior point method,PD-IPM),并结合分布式并行技术可高效求解此类问题.经典工程问题-机组组合(unit commitment,UC)为稀疏系数矩阵的结构化非线性规划,本文根据PD-IPM原理,对UC模型进行连续松弛预处理,结合快速解耦技术解耦牛顿修正方程并设计CPU-GPU协同并行算法求解子问题,最后将结果与带稠密型子问题的结构化非线性规划的求解结果进行比较和分析.实验结果显示,本文所设计的算法对于两种不同类型的结构化非线性规划求解均能获得较好的加速比.展开更多
文摘In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.
基金supported by the National Natural Science Foundation of China (Grant No.10771133)the Shanghai Leading Academic Discipline Project (Grant Nos.J50101, S30104)
文摘A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal problem via incorporating an auxiliary variable is constructed. A combined approach of logarithm barrier and quadratic penalty function is proposed to solve the problem. Based on Newton＇s method, the global convergence of interior point and line search algorithm is proven. Only a finite number of iterations is required to reach an approximate optimal solution. Numerical tests are given to show the effectiveness of the method.
基金Supported by Natural Science Foundation of Hubei Province （Grant No. 2008CDZ047）Acknowledgements Thanks my supervisor Prof. M. W. Zhang for long-last guidance during the course of study.
文摘In this paper we propose a class of new large-update primal-dual interior-point algorithms for P.（k） nonlinear complementarity problem （NCP）, which are based on a class of kernel functions investigated by Bai et al. in their recent work for linear optimization （LO）. The arguments for the algorithms are followed as Peng et al.＇s for P.（n） complementarity problem based on the self-regular functions [Peng, J., Roos, C., Terlaky, T.： Self-Regularity： A New Paradigm for Primal-Dual Interior- Point Algorithms, Princeton University Press, Princeton, 2002]. It is worth mentioning that since this class of kernel functions includes a class of non-self-regular functions as special case, so our algorithms are different from Peng et al.＇s and the corresponding analysis is simpler than theirs. The ultimate goal of the paper is to show that the algorithms based on these functions have favorable polynomial complexity.
