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The Superlinear Convergence Analysis of a Nonmonotone BFGS Algorithm on Convex Objective Functions 认领 引用 被引量：15
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作者 Gong Lin YUAN Zeng Xin WEI 《Acta Mathematica Sinica,English Series》 SCIE 2008年第1期35-42,共8页
We prove the superlinear convergence of a nonmonotone BFGS algorithm on convex objective functions under suitable conditions.
关键词 BFGS method superlinear convergence nonmonotone linesearch
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BROYDEN'S METHOD FOR SOLVING VARIATIONAL INEQUALITIES WITH GLOBAL AND SUPERLINEAR CONVERGENCE 认领 引用
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作者 Yu-fei Yang Dong-hui Li 《Journal of Computational Mathematics》 SCIE EI 2000年第3期289-304,共16页
In this paper, we establish a quasi-Newton method for solving the KKT system arising from variational inequalities. The subproblems of the proposed method are lower-dimensional mixed linear complementarity problems. A... In this paper, we establish a quasi-Newton method for solving the KKT system arising from variational inequalities. The subproblems of the proposed method are lower-dimensional mixed linear complementarity problems. A suitable line search is introduced. We show that under suitable conditions, the proposed method converges globally and superlinearly. 展开更多
关键词 Variational inequality quasi-Newton method global convergence,superlinear convergence
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SUPERLINEAR CONVERGENCE OF THE DFP ALGORITHM WITHOUT EXACT LINE SEARCH 认领 引用
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作者 濮定国 《Acta Mathematicae Applicatae Sinica》 2001年第3期430-432,共3页
关键词 DFP line SUPERLINEAR CONVERGENCE OF THE DFP ALGORITHM WITHOUT EXACT LINE SEARCH
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A superlinear convergence scheme for nonlinear fractional differential equations and its fast implement 认领 引用
4
作者 Haobo Gong Jingna Zhang +1 位作者 Hao Guo Jianfei Huang 《International Journal of Modeling, Simulation, and Scientific Computing》 EI 2019年第1期1-16,共16页
In this paper,we first construct an efficient scheme for nonlinear Caputo fractional differential equations with the initial value and the fractional degree 0<α<1.Then,the unconditional stability and the superl... In this paper,we first construct an efficient scheme for nonlinear Caputo fractional differential equations with the initial value and the fractional degree 0<α<1.Then,the unconditional stability and the superlinear convergence with the order 1+αof the proposed scheme are strictly proved and discussed.Due to the nonlocal property of fractional operators,the new scheme is time-consuming for long-time simulations.Thus,a fast implement of the proposed scheme is presented based on the sum-of-exponentials(SOE)approximation for the kernel tα−1 on the interval[h,T]in the Riemann-Liouville integral,where h is the stepsize.Some numerical experiments are provided to support the theoretical results of the new scheme and demonstrate the computational performance of its fast implement. 展开更多
关键词 Fractional differential equations nonlinear system stability superlinear convergence fast implement
A Strong Subfeasible Directions Algorithm with Superlinear Convergence 认领 引用 被引量：2
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作者 JIAN Jinbao 《Systems Science and Systems Engineering》 1996年第3期287-296,共10页
This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is mon... This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is monotonically increasing. The search directions only depend on solving one quadratic proraming and its simple correction, its line search is simple straight search and does not depend on any penalty function. Under suit assumptions, the algorithm is proved to possess global and superlinear convergence. 展开更多
关键词 Inequality constrained optimization successive quadratic programming strong subfeasible directions algorithm globl and superlinear convergence.
A SUPERLINEARLY CONVERGENT SPLITTING FEASIBLE SEQUENTIAL QUADRATIC OPTIMIZATION METHOD FOR TWO-BLOCK LARGE-SCALE SMOOTH OPTIMIZATION 认领 引用 被引量：2
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作者 简金宝 张晨 刘鹏杰 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期1-24,共24页
This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method fo... This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising. 展开更多
关键词 large scale optimization two-block smooth optimization splitting method feasible sequential quadratic optimization method superlinear convergence
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A QP-FREE AND SUPERLINEARLY CONVERGENT ALGORITHM FOR INEQUALITY CONSTRAINED OPTIMIZATIONS 认领 引用 被引量：3
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作者 徐以凡 王薇 《Acta Mathematica Scientia》 SCIE 2001年第1期121-130,共10页
In this paper, a new mixed quasi-Newton method for inequality constrained optimization problems is proposed. The feature of the method is that only the systems of linear equations are solved in each iteration, other t... In this paper, a new mixed quasi-Newton method for inequality constrained optimization problems is proposed. The feature of the method is that only the systems of linear equations are solved in each iteration, other than the quadratic programming, which decrease the amount of computations and is also efficient for large scale problem. Under some mild assumptions without the strict complementary condition., the method is globally and superlinearly convergent. 展开更多
关键词 quasi-Newton method strict complementary condition global convergence superlinear convergence
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A SUPERLINEARLY CONVERGENT TRUST REGION ALGORITHM FOR LC^1 CONSTRAINED OPTIMIZATION PROBLEMS 认领 引用 被引量：3
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作者 欧宜贵 侯定丕 《Acta Mathematica Scientia》 SCIE 2005年第1期67-80,共14页
In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with... In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view. 展开更多
关键词 LC1 optimization ODE methods trust region methods superlinear convergence
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A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS Ⅱ.LOCAL CONVERGENCE RATE AND NUMERICAL TESTS 认领 引用
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作者 XIU NAIHUA 《Applied Mathematics(A Journal of Chinese Universities)》 1995年第4期439-448,共10页
In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatu... In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective. 展开更多
关键词 Linear inequality constrained optimization trust region mothod superlinear convergence.
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A GLOBALLY AND SUPERLINEARLY CONVERGENT TRUST REGION METHOD FOR LC^1 OPTIMIZATION PROBLEMS 认领 引用 被引量：1
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作者 Zhang Liping Lai Yanlian Institute of Applied Mathematics,Academia Sinica,Beijing 100080. 《Applied Mathematics(A Journal of Chinese Universities)》 2001年第1期72-80,共9页
A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.
关键词 LC 1 optimization problem global and superlinear convergence trust region method.
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ON THE CONVERGENCE OF PARALLEL BFGS METHOD 认领 引用 被引量：1
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作者 陈忠 费浦生 《Acta Mathematica Scientia》 SCIE 1995年第3期283-294,共12页
According to the sequential BFGS method, in this paper we present an asynchronous parallel BFGS method in the case when the gradient information about the function is inexact. We assume that we have p + q processors, ... According to the sequential BFGS method, in this paper we present an asynchronous parallel BFGS method in the case when the gradient information about the function is inexact. We assume that we have p + q processors, which are divided-into two groups, the first group has p processors, the second group has q processors, the two groups are asynchronous. parallel, If we assume the objective function is twice continuously differentiable and uniformly convex, we prove the iteration converge globally to the solution, and under some additional conditions we show the method is superlinearly convergent. Finally, we show the numerical results of this algorithm. 展开更多
关键词 BFGS algorithm superlinear convergence parallel method
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SUPERLINEARLY CONVERGENT ALGORITHMS FOR STOCHASTIC TIME-FRACTIONAL EQUATIONS DRIVEN BY WHITE NOISE 认领 引用
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作者 Zhen Song Minghua Chen Jiankang Shi 《Journal of Computational Mathematics》 SCIE CSCD 2026年第3期819-842,共24页
The numerical analysis of stochastic time-fractional equations exhibits a significantly low-order convergence rate since the limited regularity of model caused by the nonlocal operator and the presence of noise.In thi... The numerical analysis of stochastic time-fractional equations exhibits a significantly low-order convergence rate since the limited regularity of model caused by the nonlocal operator and the presence of noise.In this work,we consider stochastic time-fractional equations driven by integrated white noise,where■,0<γ<1.We first establish the regularity of the mild solution.Then superlinear convergence rate■with sufficiently smallεterm in the exponent is established based on the modified twostep backward difference formula methods.Here d represents the spatial dimension,ψn denotes the approximate solution at the n-th time step,and E is the expectation operator.Numerical experiments are performed to verify the theoretical results.To the best of our knowledge,this is the first topic on the superlinear convergence analysis for the stochastic time-fractional equations with integrated white noise. 展开更多
关键词 Stochastic fractional evolution equation Integrated white noise Superlinear convergence analysis
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GLOBAL COVERGENCE OF THE NON-QUASI-NEWTON METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEMS 认领 引用 被引量：6
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作者 Liu Hongwei Wang Mingjie +1 位作者 Li Jinshan Zhang Xiangsun 《Applied Mathematics(A Journal of Chinese Universities)》 2006年第3期276-288,共13页
In this paper, the non-quasi-Newton＇s family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton＇s family is proposed. It is proved that the ... In this paper, the non-quasi-Newton＇s family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton＇s family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient. 展开更多
关键词 non-quasi-Newton method inexact line search global convergence unconstrained optimization,superlinear convergence.
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An SQP algorithm for mathematical programs with nonlinear complementarity constraints 认领 引用
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作者 朱志斌 简金宝 张聪 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第5期659-668,共10页
In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of s... In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of smooth programs to approximate the MPCC. Using an 11 penalty function, the line search assures global convergence, while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover, we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints （MPEC） when the algorithm terminates finitely. 展开更多
关键词 mathematical programs with equilibrium constraints （MPEC） SQP algorithm successive approximation global convergence superlinear convergence rate
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Smoothing Inexact Newton Method for Solving P_0-NCP Problems 认领 引用
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作者 谢伟松 武彩英 《Transactions of Tianjin University》 EI CAS 2013年第5期385-390,共6页
Based on a smoothing symmetric disturbance FB-function,a smoothing inexact Newton method for solving the nonlinear complementarity problem with P0-function was proposed.It was proved that under mild conditions,the giv... Based on a smoothing symmetric disturbance FB-function,a smoothing inexact Newton method for solving the nonlinear complementarity problem with P0-function was proposed.It was proved that under mild conditions,the given algorithm performed global and superlinear convergence without strict complementarity.For the same linear complementarity problem(LCP),the algorithm needs similar iteration times to the literature.However,its accuracy is improved by at least 4 orders with calculation time reduced by almost 50%,and the iterative number is insensitive to the size of the LCP.Moreover,fewer iterations and shorter time are required for solving the problem by using inexact Newton methods for different initial points. 展开更多
关键词 nonlinear complementarity problem smoothing Newton method global convergence superlinear convergence quadratic convergence
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Nonmonotone Adaptive Trust Region Algorithms with Indefinite Dogleg Path for Unconstrained Minimization 认领 引用 被引量：13
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作者 陈俊 孙文瑜 《Northeastern Mathematical Journal》 2008年第1期19-30,共12页
In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the ... In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the monotone sequence, the nonmonotone sequence of function values are employed. With the adaptive technique, the radius of trust region △k can be adjusted automatically to improve the efficiency of trust region methods. By means of the Bunch-Parlett factorization, we construct a method with indefinite dogleg path for solving the trust region subproblem which can handle the indefinite approximate Hessian Bk. The convergence properties of the algorithm are established. Finally, detailed numerical results are reported to show that our algorithm is efficient. 展开更多
关键词 nonmonotone trust region method adaptive method indefinite dogleg path unconstrained minimization global convergence superlinear convergence
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A Superlinerly Convergent ODE-type Trust Region Algorithm for LC^1 Optimization Problems 认领 引用 被引量：5
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作者 OUYi-gui HOUDing-pi 《Chinese Quarterly Journal of Mathematics》 2003年第2期140-145,共6页
In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at eac... In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions. 展开更多
关键词 LC1 optimization ODE methods trust region algorithm superlinear convergence
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A SQP METHOD FOR GENERAL NONLINEAR COMPLEMENTARITY PROBLEMS 认领 引用
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作者 Xiu Naihua.Dept.of Appl.Math.,Northern Jiaotong Univ.,Beijing 100044. Email:nhxiu@center.njtu.edu.cn 《Applied Mathematics(A Journal of Chinese Universities)》 2000年第4期433-442,共10页
In this paper,the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints,and a SQP algorithm for this reformulation based on a damped Gauss Newton type method is p... In this paper,the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints,and a SQP algorithm for this reformulation based on a damped Gauss Newton type method is presented.It is shown that the algorithm is globally and locally superlinearly (quadratically) convergent without the assumption of monotonicity. 展开更多
关键词 Nonlinear complementarity problem SQP method superlinear convergence quadratic convergence.
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An Improved Quasi-Newton Method for Unconstrained Optimization 认领 引用 被引量：1
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作者 Fei Pusheng Chen Zhong 《Wuhan University Journal of Natural Sciences》 CAS 1996年第1期35-37,共3页
We present an improved method. If we assume that the objective function is twice continuously differentiable and uniformly convex, we discuss global and superlinear convergence of the improved quasi-Newton method.
关键词 quasi-Newton method,superlinear convergence unconstrained optimization
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A New Nonmonotone Adaptive Trust Region Method 认领 引用 被引量：1
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作者 Yang Zhang Quanming Ji Qinghua Zhou 《Journal of Applied Mathematics and Physics》 2021年第12期3102-3114,共13页
The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we ... The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we combine a popular nonmonotone technique with an adaptive trust region algorithm. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some appropriate conditions, we show that the new algorithm has good global convergence and superlinear convergence. 展开更多
关键词 Unconstrained Optimization Trust Region Method Nonmonotone Technique Global Convergence Superlinear Convergence
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