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A Primal-dual Interior Point Method for Nonlinear Programming 认领 引用 被引量：1
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作者 张珊 姜志侠 《Northeastern Mathematical Journal》 2008年第3期275-282,共8页
In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local ... In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way. 展开更多
关键词 primal-dual interior point algorithm merit function global convergence nonlinear programming
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Novel Kernel Function With a Hyperbolic Barrier Term to Primal-dual Interior Point Algorithm for SDP Problems 认领 引用 被引量：1
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作者 Imene TOUIL Wided CHIKOUCHE 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2022年第1期44-67,共24页
In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions.... In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions.We prove that the interior-point algorithm based on the new kernel function meets O(n3/4 logε)iterations as the worst case complexity bound for the large-update method.This coincides with the complexity bound obtained by the first kernel function with a trigonometric barrier term proposed by El Ghami et al.in2012,and improves with a factor n(1/4)the obtained iteration bound based on the classic kernel function.We present some numerical simulations which show the effectiveness of the algorithm developed in this paper. 展开更多
关键词 Linear Semidefinite Programming Primal-Dual Interior Point Methods Hyperbolic Kernel Function Complexity Analysis Large and small-update methods
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A Primal-Dual Infeasible-Interior-Point Algorithm for Multiple Objective Linear Programming Problems 认领 引用
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作者 HUANG Hui FEI Pu-sheng YUAN Yuan 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第2期351-354,共4页
A primal-dual infeasible interior point algorithm for multiple objective linear programming(MOLP)problems was presented.In contrast to the current MOLP algorithm.moving through the interior of polytope but not confini... A primal-dual infeasible interior point algorithm for multiple objective linear programming(MOLP)problems was presented.In contrast to the current MOLP algorithm.moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size,so providing the potential to dramatically improve the practical computation effectiveness. 展开更多
关键词 multiple objective linear programming primal dual infeasible interior point algorithm
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AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM 认领 引用 被引量：12
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作者 迟晓妮 刘三阳 《Acta Mathematica Scientia》 SCIE 2008年第3期551-559,共9页
A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorith... A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP. 展开更多
关键词 Second-order cone programming, infeasible-interior-point algorithm, predictor-corrector algorithm global convergence
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A SYMMETRIC PRIMAL-DUAL ALGORITHMIC FRAMEWORK FOR SADDLE POINT PROBLEMS 认领 引用
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作者 Hongjin He Kai Wang Jintao Yu 《Journal of Computational Mathematics》 SCIE CSCD 2026年第4期1049-1082,共34页
In this paper,we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning.Our algorithmic framework updates the ... In this paper,we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning.Our algorithmic framework updates the primal variable between the twice calculations of the dual variable,thereby appearing a symmetric iterative scheme,which is accordingly called the symmetric primal-dual algorithm(SPIDA).It is noteworthy that the subproblems of our SPIDA are equipped with Bregman proximal regularization terms,which make SPIDA versatile in the sense that it enjoys an algorithmic framework to understand the iterative schemes of some existing algorithms,such as the classical augmented Lagrangian method(ALM),linearized ALM,and Jacobian splitting algorithms for linearly constrained optimization problems.Besides,our algorithmic framework allows us to derive some customized versions so that SPIDA works as efficiently as possible for structured optimization problems.Theoretically,under some mild conditions,we prove the global convergence of SPIDA and estimate the linear convergence rate under a generalized error bound condition defined by Bregman distance.Finally,a series of numerical experiments on the basis pursuit,robust principal component analysis,and image restoration demonstrate that our SPIDA works well on synthetic and real-world datasets. 展开更多
关键词 Primal-dual algorithm Saddle point problem Bregman distance Augmented Lagrangian method Convex programming
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Predictor-corrector interior-point algorithm for linearly constrained convex programming 认领 引用
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作者 LIANG Xi-ming 《Journal of Central South University》 SCIE EI CAS 2001年第3期208-212,共5页
Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming.Interior-po int method is one of the most effective choices for linear programming.In th... Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming.Interior-po int method is one of the most effective choices for linear programming.In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed.In eac h iteration,the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory.Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required.It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method.Numerical experiments on twenty-six standard test problems are made.The result s show that the proposed algorithm is stable and robust. 展开更多
关键词 linearly constrained convex programming predictor corrector interior point algorithm numerical experiment
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A POSITIVE INTERIOR-POINT ALGORITHM FOR NONLINEAR COMPLEMENTARITY PROBLEMS 认领 引用
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作者 马昌凤 梁国平 陈新美 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第3期355-362,共8页
A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theore... A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theorems of the algorithm is established.In addition,some numerical results are reported. 展开更多
关键词 nonlinear complementarity problems positive interior-point algorithm non-smooth equations
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A Wide Neighborhood Arc-Search Interior-Point Algorithm for Convex Quadratic Programming 认领 引用 被引量：2
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作者 YUAN Beibei ZHANG Mingwang HUANG Zhengwei 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2017年第6期465-471,共7页
In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the ent... In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the entire central path. The favorable polynomial complexity bound of the algorithm is obtained, namely O（nlog（（ x^0）~TS^0/ε）） which is as good as the linear programming analogue. Finally, the numerical experiments show that the proposed algorithm is efficient. 展开更多
关键词 arc-search interior-point algorithm polynomial complexity convex quadratic programming
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Interior-Point Algorithm for Linear Optimization Based on a New Kernel Function 认领 引用 被引量：2
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作者 CHEN Donghai ZHANG Mingwang LI Weihua 《Wuhan University Journal of Natural Sciences》 CAS 2012年第1期12-18,共7页
In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barr... In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions. 展开更多
关键词 linear optimization interior-point algorithms pri- mal-dual methods kernel function polynomial complexity
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An Improved Affine-Scaling Interior Point Algorithm for Linear Programming 认领 引用 被引量：1
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作者 Douglas Kwasi Boah Stephen Boakye Twum 《Journal of Applied Mathematics and Physics》 2019年第10期2531-2536,共6页
In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. Th... In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. The proposed algorithm is accurate, faster and therefore reduces the number of iterations required to obtain an optimal solution of a given Linear Programming problem as compared to the already existing Affine-Scaling Interior Point Algorithm. The algorithm can be very useful for development of faster software packages for solving linear programming problems using the interior-point methods. 展开更多
关键词 Interior-Point Methods Affine-Scaling Interior Point Algorithm Optimal Solution Linear Programming Initial Feasible Trial Solution
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A predictor-corrector interior-point algorithmfor monotone variational inequality problems 认领 引用 被引量：2
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作者 梁昔明 钱积新 《Journal of Zhejiang University Science》 2002年第3期321-325,共5页
Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the a... Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the authors give a predictor corrector interior point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level 1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented. 展开更多
关键词 Variational inequality problems(VIP) Predictor corrector interior point algorithm Numerical experiments
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Optimal Adjustment Algorithm for pCoordinates and The Starting Point in Interior Point Methods 认领 引用 被引量：1
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作者 Carla T. L. S. Ghidini Aurelio R. L. Oliveira Jair Silva 《American Journal of Operations Research》 2011年第4期191-202,共12页
Optimal adjustment algorithm for p coordinates is a generalization of the optimal pair adjustment algorithm for linear programming, which in turn is based on von Neumann’s algorithm. Its main advantages are simplicit... Optimal adjustment algorithm for p coordinates is a generalization of the optimal pair adjustment algorithm for linear programming, which in turn is based on von Neumann’s algorithm. Its main advantages are simplicity and quick progress in the early iterations. In this work, to accelerate the convergence of the interior point method, few iterations of this generalized algorithm are applied to the Mehrotra’s heuristic, which determines the starting point for the interior point method in the PCx software. Computational experiments in a set of linear programming problems have shown that this approach reduces the total number of iterations and the running time for many of them, including large-scale ones. 展开更多
关键词 Von Neumann’s Algorithm Mehrotra’s Heuristic Interior Point Methods Linear Programming
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基于新代数等价变换求解Fisher市场均衡问题的全牛顿步内点算法 认领 引用
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作者 迟晓妮 张璐 +1 位作者 刘三阳 张所滨 《工程数学学报》 北大核心 2026年第1期1-14,共14页
权互补问题是互补问题的一类重要推广,当权向量为零向量时,该问题就化为互补问题。非零权向量的存在使得权互补问题的理论和算法更为复杂。权互补问题的应用广泛,科学、经济等领域中的一大类均衡问题都可以转化为权互补问题进行求解,比... 权互补问题是互补问题的一类重要推广,当权向量为零向量时,该问题就化为互补问题。非零权向量的存在使得权互补问题的理论和算法更为复杂。权互补问题的应用广泛,科学、经济等领域中的一大类均衡问题都可以转化为权互补问题进行求解,比如Fisher市场均衡问题可化为一种斜对称的权互补问题。提出了一种求解Fisher市场均衡问题的线性权互补模型的新全牛顿步内点算法。基于中心方程的新代数等价变换形式,运用核函数φ(t)=t2计算搜索方向。该核函数首次被用于求解线性权互补问题。算法每次迭代仅使用一个全牛顿步,无需进行线搜索,节省运行内存。证明算法的收敛性及多项式复杂度,最后通过数值算例验证了算法的有效性。 展开更多
关键词 线性权互补问题 Fisher市场均衡 全牛顿步 内点算法 核函数 代数等价变换
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A PRIMAL-DUAL FIXED POINT ALGORITHM FOR MULTI-BLOCK CONVEX MINIMIZATION 认领 引用 被引量：2
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作者 Peijun Chen Jianguo Huang Xiaoqun Zhang 《Journal of Computational Mathematics》 SCIE CSCD 2016年第6期723-738,共16页
We have proposed a primal-dual fixed point algorithm （PDFP） for solving minimiza- tion of the sum of three convex separable functions, which involves a smooth function with Lipschitz continuous gradient, a linear co... We have proposed a primal-dual fixed point algorithm （PDFP） for solving minimiza- tion of the sum of three convex separable functions, which involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function, and a nonsmooth function. Compared with similar works, the parameters in PDFP are easier to choose and are allowed in a relatively larger range. We will extend PDFP to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP algorithm to multi-block prob- lems and illustrates how practical and fully splitting schemes can be derived, especially for parallel implementation of large scale problems. The connections and comparisons to the alternating direction method of multiplier （ADMM） are also present. We demonstrate how different algorithms can be obtained by splitting the problems in different ways through the classic example of sparsity regularized least square model with constraint. In particular, for a class of linearly constrained problems, which are of great interest in the context of multi-block ADMM, can be also solved by PDFP with a guarantee of convergence. Finally, some experiments are provided to illustrate the performance of several schemes derived by the PDFP algorithm. 展开更多
关键词 Primal-dual fixed point algorithm Multi-block optimization problems.
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线性规划求解的自协调对偶障碍函数内点算法 认领 引用
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作者 曹邦兴 《新乡学院学报》 2026年第6期1-4,共4页
基于小步校正的原始对偶内点算法的理论复杂度低于大步校正算法,但实践性较差,实际计算效果并不理想。针对这种情况,给出了线性规划中原始对偶内点算法的一种新的障碍函数(核函数)。证明了该函数具有自协调性质,分析了基于该障碍函数内... 基于小步校正的原始对偶内点算法的理论复杂度低于大步校正算法,但实践性较差,实际计算效果并不理想。针对这种情况,给出了线性规划中原始对偶内点算法的一种新的障碍函数(核函数)。证明了该函数具有自协调性质,分析了基于该障碍函数内点算法的搜索方向和中心路径实现方法,并给出了其小步校正算法的具体实施步骤,得出了其理论迭代界与经典障碍函数的理论迭代界都为O(√nlnε)的结构,但数值算例表明其计算效果明显优于经典障碍函数。 展开更多
关键词 线性规划 原始对偶内点算法 自协调对偶障碍函数 迭代界
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负载电压约束下SIMO无线电能传输系统效率优化方法研究 认领 引用
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作者 李旺 王琪 刘佳伟 《电机与控制应用》 2026年第2期158-167,共10页
【目的】解决单输入多输出无线电能传输(SIMO-WPT)系统在多负载电压约束下全局效率优化难题。【方法】本文构建了包含线圈损耗、二极管损耗的全链路传输效率模型,分析了发射侧移相与接收侧Buck-Boost的控制机制,提出了一种遗传—内点协... 【目的】解决单输入多输出无线电能传输(SIMO-WPT)系统在多负载电压约束下全局效率优化难题。【方法】本文构建了包含线圈损耗、二极管损耗的全链路传输效率模型,分析了发射侧移相与接收侧Buck-Boost的控制机制,提出了一种遗传—内点协同优化算法。该算法结合了遗传算法的全局寻优和内点法的快速收敛,避免了局部最优和初始点敏感问题。【结果】仿真与实物试验结果表明,本文所提遗传—内点协同优化算法相较于传统方案寻优速度更快,且严格收敛于全局效率最优点。【结论】本文所建效率模型覆盖WPT系统关键损耗环节,能适配不同负载数量、电压约束及线圈参数场景,具备较强推广价值。本文所提遗传—内点协同优化算法有效解决了负载电压约束下SIMO-WPT系统的全局高效优化难题,为同类WPT系统的效率设计提供了可行参考。 展开更多
关键词 单输入多输出无线电能传输 电压约束 效率优化 遗传—内点协同优化算法
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考虑断面耦合和越限控制的大电网新能源跨区消纳能力优化方法 认领 引用 被引量：1
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作者 李群山 黄牧涛 +3 位作者 曾令康 魏聪颖 高素花 陈兴邦 《武汉大学学报（工学版）》 CAS CSCD 北大核心 2025年第8期1246-1255,共10页
针对新能源消纳困难和大规模新能源接入对新型电力系统电力平衡带来的挑战,将集火、水、光、储于一体的特高压复杂大电网划分为多个分区电网,从系统整体优化的视角,将目标省网内常规机组发电调减量总和最大作为目标函数,综合考虑功率平... 针对新能源消纳困难和大规模新能源接入对新型电力系统电力平衡带来的挑战,将集火、水、光、储于一体的特高压复杂大电网划分为多个分区电网,从系统整体优化的视角,将目标省网内常规机组发电调减量总和最大作为目标函数,综合考虑功率平衡、常规机组旋转备用容量、输电断面约束、省间交流断面受电计划约束、断面耦合约束等电力系统安全稳定运行约束,提出计及断面耦合和重载越限控制的复杂大电网新能源跨区消纳能力评估模型;然后分别应用单纯形法、内点法、模拟退化算法、白鲸优化算法和蜂群算法求解模型,综合计算大电网在日内未来15 min通过常规发电机组发电量调整所能达到的最大新能源发电消纳量,并提出各类型电源的综合调节优化方案。以某区域电网为例进行模型及求解方法验证,仿真结果显示,因电力系统规模庞大和断面间耦合关系复杂,启发式智能优化算法存在运行时间较长、收敛速度较慢、搜索精度不高等问题,而内点法收敛迅速、鲁棒性强、对初值的选择不敏感,具有更好的稳定性和计算效率,可为复杂大电网优化调度运行提供有效实用的支撑。 展开更多
关键词 复杂大电网 新能源消纳能力 断面耦合控制 断面重载越限 内点法 启发式智能优化算法
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Correction of array failure using grey wolf optimizer hybridized with an interior point algorithm 认领 引用 被引量：3
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作者 Shafqat Ullah KHAN M.K.A.RAHIM Liaqat ALI 《Frontiers of Information Technology & Electronic Engineering》 SCIE EI CSCD 2018年第9期1191-1202,共12页
We design a grey wolf optimizer hybridized with an interior point algorithm to correct a faulty antenna array. If a single sensor fails, the radiation power pattern of the entire array is disturbed in terms of sidelob... We design a grey wolf optimizer hybridized with an interior point algorithm to correct a faulty antenna array. If a single sensor fails, the radiation power pattern of the entire array is disturbed in terms of sidelobe level(SLL) and null depth level(NDL), and nulls are damaged and shifted from their original locations. All these issues can be solved by designing a new fitness function to reduce the error between the preferred and expected radiation power patterns and the null limitations. The hybrid algorithm has been designed to control the array's faulty radiation power pattern. Antenna arrays composed of 21 sensors are used in an example simulation scenario. The MATLAB simulation results confirm the good performance of the proposed method, compared with the existing methods in terms of SLL and NDL. 展开更多
关键词 Failure correction Grey wolf optimizer Interior point algorithm Sidelobes Deeper null depth level
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考虑原油采购选择的混炼加工优化 认领 引用
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作者 董丰莲 李鹏 +3 位作者 魏志伟 孙鑫 徐赫锴 何畅 《化工进展》 EI CAS CSCD 北大核心 2025年第8期4648-4656,共9页
目前,原油采购和混炼加工方案多采用人工经验或数学规划方法进行决策,存在求解时间过长以及无法统筹考虑全局性等问题。针对炼化场景下的典型混炼工艺和原油采购要求,结合“P模型”的概念建立了混合整数非线性模型,并根据整数变量的特... 目前,原油采购和混炼加工方案多采用人工经验或数学规划方法进行决策,存在求解时间过长以及无法统筹考虑全局性等问题。针对炼化场景下的典型混炼工艺和原油采购要求,结合“P模型”的概念建立了混合整数非线性模型,并根据整数变量的特性设计了基于p范数和内点法的迭代求解算法。结果表明,在10种原油、54种物性、58套加工装置的优化背景下,与商用求解器优化结果相比,采用以上方法可以在短时间内找到一个经济效益更好的原油采购加工方案并且在多个算例下均展现出了更好的鲁棒性。 展开更多
关键词 优化 算法 石油 混炼 双线性 内点法 范数平滑
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Path-following interior point algorithms for the Cartesian P_*(κ)-LCP over symmetric cones 认领 引用 被引量：6
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作者 LUO ZiYan XIU NaiHua 《Science China Mathematics》 2009年第8期1769-1784,共16页
In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condi... In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms. 展开更多
关键词 Cartesian P *(κ)-property symmetric cone linear complementarity problem path-following interior point algorithm global convergence complexity 90C33 90C51
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