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A class of polynomial primal-dual interior-point algorithms for semidefinite optimization 认领 引用 被引量：6
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作者 王国强 白延琴 《Journal of Shanghai University(English Edition)》 2006年第3期198-207,共10页
In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to... In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to its growth term increasing linearly. Some new analysis tools were developed which can be used to deal with complexity ＂analysis of the algorithms which use analogous strategy in [5] to design the search directions for the Newton system. The complexity bounds for the algorithms with large- and small-update methodswere obtained, namely,O（qn^（p＋q/q（P＋1）log n/ε and O（q^2√n）log n/ε,respectlvely. 展开更多
关键词 semidefinite optimization （SDO） primal-dual interior-point methods large- and small-update methods 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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AN ACCELERATED PRECONDITIONED PRIMAL-DUAL GRADIENT ALGORITHM FOR NONCONVEX COMPOSITE OPTIMIZATION PROBLEMS WITH APPLICATIONS 认领 引用
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作者 Xian-Jun Long Jia-Lin Nie +1 位作者 Gao-Xi Li Zai-Yun Peng 《Journal of Computational Mathematics》 SCIE CSCD 2026年第6期1867-1889,共23页
In this paper,we consider a class of three-composite nonconvex optimization problems,in which the nonsmooth function is further composed with a linear operator.This problem has many applications such as sparse signal ... In this paper,we consider a class of three-composite nonconvex optimization problems,in which the nonsmooth function is further composed with a linear operator.This problem has many applications such as sparse signal recovery,image processing and machine learning.Based on the conjugate duality theory,we present an accelerated preconditioned primal-dual gradient algorithm for this problem.Compared with the existing algorithms,our algorithm only needs to calculate the proximal mapping of the conjugate function h*which is always convex and lower semicontinuous and it does not need to calculate the proximal mapping of nonconvex functions.This may significantly reduce the computation load.We prove that the sequence generated by the proposed algorithm globally converges to a critical point when the function satisfies the Kurdyka-Lojasiewicz property.We also obtain the convergence rate of the proposed algorithm.Finally,numerical results on sparse signal recovery and image processing illustrate the efficiency and competitiveness of the proposed algorithm. 展开更多
关键词 Nonconvex Composite Optimization Primal-dual Algorithm Convergence Sparse Signal Recovery Image Processing
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A New Kernel Function Yielding the Best Known Iteration Bounds for Primal-Dual Interior-Point Algorithms 认领 引用 被引量：8
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作者 Yan Qin BAI Jin LiGUO Cornelis ROOS 《Acta Mathematica Sinica,English Series》 SCIE 2009年第12期2169-2178,共10页
Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields ... Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields an algorithm with the best known complexity bound for both large- and small-update methods. 展开更多
关键词 linear optimization interior-point method primal-dual method large-update method polynomial 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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A Class of New Large-Update Primal-Dual Interior-Point Algorithms for P*(k)Nonlinear Complementarity Problems 认领 引用
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作者 Hua Ping CHEN Ming Wang ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第10期1979-1994,共16页
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 th... 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
关键词 Large-update method interior-point algorithm nonlinear complementarity problem non-self-regular function polynomial complexity
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A Primal-Dual SGD Algorithm for Distributed Nonconvex Optimization 认领 引用 被引量：9
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作者 Xinlei Yi Shengjun Zhang +2 位作者 Tao Yang Tianyou Chai Karl Henrik Johansson 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2022年第5期812-833,共22页
The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is considered.This problem is an important component of... The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is considered.This problem is an important component of many machine learning techniques with data parallelism,such as deep learning and federated learning.We propose a distributed primal-dual stochastic gradient descent(SGD)algorithm,suitable for arbitrarily connected communication networks and any smooth(possibly nonconvex)cost functions.We show that the proposed algorithm achieves the linear speedup convergence rate O(1/(√nT))for general nonconvex cost functions and the linear speedup convergence rate O(1/(nT)) when the global cost function satisfies the Polyak-Lojasiewicz(P-L)condition,where T is the total number of iterations.We also show that the output of the proposed algorithm with constant parameters linearly converges to a neighborhood of a global optimum.We demonstrate through numerical experiments the efficiency of our algorithm in comparison with the baseline centralized SGD and recently proposed distributed SGD algorithms. 展开更多
关键词 Distributed nonconvex optimization linear speedup Polyak-Lojasiewicz(P-L)condition primal-dual algorithm stochastic gradient descent
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First-order primal-dual algorithm for sparse-view neutron computed tomography-based three-dimensional image reconstruction 认领 引用 被引量：4
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作者 Yang Liu Teng-Fei Zhu +1 位作者 Zhi Luo Xiao-Ping Ouyang 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2023年第8期35-53,共19页
Neutron computed tomography(NCT)is widely used as a noninvasive measurement technique in nuclear engineering,thermal hydraulics,and cultural heritage.The neutron source intensity of NCT is usually low and the scan tim... Neutron computed tomography(NCT)is widely used as a noninvasive measurement technique in nuclear engineering,thermal hydraulics,and cultural heritage.The neutron source intensity of NCT is usually low and the scan time is long,resulting in a projection image containing severe noise.To reduce the scanning time and increase the image reconstruction quality,an effective reconstruction algorithm must be selected.In CT image reconstruction,the reconstruction algorithms can be divided into three categories:analytical algorithms,iterative algorithms,and deep learning.Because the analytical algorithm requires complete projection data,it is not suitable for reconstruction in harsh environments,such as strong radia-tion,high temperature,and high pressure.Deep learning requires large amounts of data and complex models,which cannot be easily deployed,as well as has a high computational complexity and poor interpretability.Therefore,this paper proposes the OS-SART-PDTV iterative algorithm,which uses the ordered subset simultaneous algebraic reconstruction technique(OS-SART)algorithm to reconstruct the image and the first-order primal–dual algorithm to solve the total variation(PDTV),for sparse-view NCT three-dimensional reconstruction.The novel algorithm was compared with other algorithms(FBP,OS-SART-TV,OS-SART-AwTV,and OS-SART-FGPTV)by simulating the experimental data and actual neutron projection experiments.The reconstruction results demonstrate that the proposed algorithm outperforms the FBP,OS-SART-TV,OS-SART-AwTV,and OS-SART-FGPTV algorithms in terms of preserving edge structure,denoising,and suppressing artifacts. 展开更多
关键词 NCT First-order primal-dual algorithm OS-SART Total variation Sparse-view
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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 Primal-Dual Simplex Algorithm for Solving Linear Programming Problems with Symmetric Trapezoidal Fuzzy Numbers 认领 引用 被引量：2
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作者 Ali Ebrahimnejad 《Applied Mathematics》 2011年第6期676-684,共9页
Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simpl... Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach. 展开更多
关键词 Fuzzy Linear Programming Fuzzy Arithmetic Fuzzy Orders Primal-Dual Simplex Algorithm
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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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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 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 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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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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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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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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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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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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