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A POLYNOMIAL PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING 认领 引用 被引量：6
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作者 余谦 黄崇超 江燕 《Acta Mathematica Scientia》 SCIE 2006年第2期265-270,共6页
This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one c... This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O（√nL） iteration complexity which is the best result for convex quadratic programming so far. 展开更多
关键词 Convex quadratic programming predictor-corrector interior-point algorithm
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A PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING 认领 引用
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作者 Liang Ximing +1 位作者 Qian Jixin 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 2002年第1期52-62,共11页
The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off betwee... The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interiorpoint method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made. 展开更多
关键词 convex quadratic programming, interior-point methods, predictor-corrector algorithms, numerical experiments.
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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 Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on Algebraic Equivalent Transformation 认领 引用
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作者 Jing GE Mingwang ZHANG Panjie TIAN 《Journal of Mathematical Research with Applications》 CSCD 2025年第4期555-568,共14页
In this paper,we propose a new full-Newton step feasible interior-point algorithm for the special weighted linear complementarity problems.The proposed algorithm employs the technique of algebraic equivalent transform... In this paper,we propose a new full-Newton step feasible interior-point algorithm for the special weighted linear complementarity problems.The proposed algorithm employs the technique of algebraic equivalent transformation to derive the search direction.It is shown that the proximity measure reduces quadratically at each iteration.Moreover,the iteration bound of the algorithm is as good as the best-known polynomial complexity for these types of problems.Furthermore,numerical results are presented to show the efficiency of the proposed algorithm. 展开更多
关键词 interior-point algorithm weighted linear complementarity problem algebraic equivalent transformation search direction iteration complexity
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A Wide-Neighborhood Predictor-Corrector Interior-Point Algorithm for Linear Complementarity Problems 认领 引用 被引量：1
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作者 Mohammad Pirhaji Hossein Mansouri Maryam Zangiabadi 《Journal of the Operations Research Society of China》 EI CSCD 2018年第4期529-543,共15页
In this paper,a wide-neighborhood predictor-corrector feasible interiorpoint algorithm for linear complementarity problems is proposed.The algorithm is based on using the classical affine scaling direction as a part i... In this paper,a wide-neighborhood predictor-corrector feasible interiorpoint algorithm for linear complementarity problems is proposed.The algorithm is based on using the classical affine scaling direction as a part in a corrector step,not in a predictor step.The convergence analysis of the algorithm is shown,and it is proved that the algorithm has the polynomial complexity O(√n logε−1)which coincides with the best known iteration bound for this class of mathematical problems.The numerical results indicate the efficiency of the algorithm. 展开更多
关键词 Linear complementarity problems Predictor-corrector algorithm Polynomial complexity
Two new predictor-corrector algorithms for second-order cone programming 认领 引用 被引量：1
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作者 曾友芳 白延琴 +1 位作者 简金宝 唐春明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第4期521-532,共12页
Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algor... Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton （AHO） directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O（rln（εo/ε）） is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective. 展开更多
关键词 second-order cone programming infeasible interior-point algorithm predictor-corrector algorithm global convergence complexity analysis
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A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function 认领 引用 被引量：2
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作者 GENG Jie ZHANG Mingwang ZHU Dechun 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2024年第1期29-37,共9页
In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear ... In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method. 展开更多
关键词 interior-point algorithm weighted linear complementarity problem full-Newton step kernel function iteration complexity
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A new primal-dual path-following interior-point algorithm for linearly constrained convex optimization 认领 引用 被引量：1
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作者 张敏 白延琴 王国强 《Journal of Shanghai University(English Edition)》 2008年第6期475-480,共6页
In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions a... In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions and the strategy of the central path.At each iteration, only full-Newton steps are used.Finally, the favorable polynomial complexity bound for the algorithm with the small-update method is deserved, namely, O(√n log n /ε). 展开更多
关键词 linearly constrained convex optimization （LCCO） interior-point algorithm small-update method polynomial complexity
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PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS 认领 引用
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作者 丁协平 林炎诚 姚任之 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第9期1157-1164,共8页
A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems... A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings 展开更多
关键词 generalized mixed implicit quasi-equilibrium problem auxiliary variational inequality predictor-corrector iterative algorithms partially relaxed implicit strong monotonicity
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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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Polynomial Complexity Bounds of Mehrotra-type Predictor-corrector Algorithms for Linear Programming over Symmetric Cones 认领 引用
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作者 刘长河 尚有林 李振国 《Chinese Quarterly Journal of Mathematics》 2015年第4期475-494,共20页
We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the s... We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples. 展开更多
关键词 linear programming symmetric cone Euclidean Jordan algebra interior-point methods Mehrotra-type algorithm polynomial complexity
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New Mehrotra's second order predictor-corrector algorithm for P_*(κ)linear complementarity problems 认领 引用
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作者 Mingwang Zhang Yanli Lv 《Journal of Systems Engineering and Electronics》 SCIE EI 2010年第4期705-712,共8页
It has been shown in various papers that most interior-point algorithms for linear optimization and their analysis can be generalized to P_*(κ)linear complementarity problems.This paper presents an extension of the r... It has been shown in various papers that most interior-point algorithms for linear optimization and their analysis can be generalized to P_*(κ)linear complementarity problems.This paper presents an extension of the recent variant of Mehrotra's second order algorithm for linear optimijation.It is shown that the iteration-complexity bound of the algorithm is O(4κ+3)√14κ+5 nlog(x0)Ts0/ε,which is similar to that of the corresponding algorithm for linear optimization. 展开更多
关键词 linear complementarity problem P_*(κ)-matrix Mehrotra-type predictor-corrector algorithm polynomial complexity.
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SOLVING CONVEX QUADRATIC PROGRAMMING BY POTENTIAL-REDUCTION INTERIOR-POINT ALGORITHM 认领 引用
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作者 LIANG Xi-ming MA Long-hua QIAN Ji-xin 《Journal of Zhejiang University Science》 2001年第1期67-71,共5页
The solution of quadratic programming problems is an important issue in the field of mathematical programming and industrial applications.In this paper,we solve convex quadratic programming by a potential-reduction in... The solution of quadratic programming problems is an important issue in the field of mathematical programming and industrial applications.In this paper,we solve convex quadratic programming by a potential-reduction interior-point algorithm.It is proved that the potential-reduction interior-point algorithm is globally convergent.Some numerical experiments were made. 展开更多
关键词 potential-reduction interior-point algorithm convex quadratic programming convergence numerical experiments
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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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Complexity analysis of interior-point algorithm based on a new kernel function for semidefinite optimization 认领 引用 被引量：3
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作者 钱忠根 白延琴 王国强 《Journal of Shanghai University(English Edition)》 2008年第5期388-394,共7页
Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with si... Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with simple algebraic expression is proposed. Based on this kernel function, a primal-dual interior-point methods （IPMs） for semidefinite optimization （SDO） is designed. And the iteration complexity of the algorithm as O（n^3/4 log n/ε） with large-updates is established. The resulting bound is better than the classical kernel function, with its iteration complexity O（n log n/ε） in large-updates case. 展开更多
关键词 interior-point algorithm primal-dual method semidefinite optimization （SDO） polynomial complexity
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Primal-Dual Interior-Point Algorithms with Dynamic Step-Size Based on Kernel Functions for Linear Programming 认领 引用 被引量：3
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作者 钱忠根 白延琴 《Journal of Shanghai University(English Edition)》 2005年第5期391-396,共6页
In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming （LP） problems. The algorithms are based on a few kernel functions, including both serf-regular functio... In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming （LP） problems. The algorithms are based on a few kernel functions, including both serf-regular functions and non-serf-regular ones. The dynamic step size is compared with fixed step size for the algorithms in inner iteration of Newton step. Numerical tests show that the algorithms with dynaraic step size are more efficient than those with fixed step size. 展开更多
关键词 linear programming （LP） interior-point algorithm small-update method large-update method.
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A New Second-Order Mehrotra-Type Predictor-Corrector Algorithm for SDO 认领 引用
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作者 HUANG Fangyan ZHANG Mingwang HUANG Zhengwei 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2016年第2期99-109,共11页
In Zhang’s recent works,a second-order Mehrotra-type predictor-corrector algorithm for linear optimization was extended to semidefinite optimization and derived that the algorithm for semidefinite optimization had3/2... In Zhang’s recent works,a second-order Mehrotra-type predictor-corrector algorithm for linear optimization was extended to semidefinite optimization and derived that the algorithm for semidefinite optimization had3/2 0 T 0O（nlog（X）gS/e）iteration complexity based on the NT direction as Newton search direction.In this paper,we extend the second-order Mehrotra-type predictor-corrector algorithm for linear optimization to semidefinite optimization and discuss the polynomial convergence of the algorithm by modifying the corrector direction and new iterates.It is proved that the iteration complexity is reduced to0 0O（nlog XgS/e）,which coincides with the currently best iteration bound of Mehrotra-type predictor-corrector algorithm for semidefinite optimization. 展开更多
关键词 Mehrotra-type algorithm predictor-corrector methods semidefinite optimization
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An Explicit-Implicit Predictor-Corrector Domain Decomposition Method for Time Dependent Multi-Dimensional Convection Diffusion Equations 认领 引用 被引量：1
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作者 Liyong Zhu Guangwei Yuan Qiang Du 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2009年第3期301-325,共25页
The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain ... The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments. 展开更多
关键词 Convection diffusion equation parallel algorithm domain decomposition modifiedupwind differences predictor-corrector explicit-implicit scheme convergence analysis.
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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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