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Constructive Theory of Designing Optimal Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations
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作者 Tugal Zhanlav Khuder Otgondorj Renchin-Ochir Mijiddorj 《American Journal of Computational Mathematics》 2020年第1期100-117,共18页
This paper stresses the theoretical nature of constructing the optimal derivative-free iterations. We give necessary and sufficient conditions for derivative-free three-point iterations with the eighth-order of conver... This paper stresses the theoretical nature of constructing the optimal derivative-free iterations. We give necessary and sufficient conditions for derivative-free three-point iterations with the eighth-order of convergence. We also establish the connection of derivative-free and derivative presence three-point iterations. The use of the sufficient convergence conditions allows us to design wide class of optimal derivative-free iterations. The proposed family of iterations includes not only existing methods but also new methods with a higher order of convergence. 展开更多
关键词 Multipoint methods derivative-free methods Order of CONVERGENCE
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An Efficient Pattern Search Method 被引量:1
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作者 Xiaoli Zhang Qinghua Zhou Yue Wang 《Journal of Applied Mathematics and Physics》 2013年第4期68-72,共5页
Pattern search algorithms is one of most frequently used methods which were designed to solve the derivative-free optimization problems. Such methods get growing need with the development of science, engineering, econ... Pattern search algorithms is one of most frequently used methods which were designed to solve the derivative-free optimization problems. Such methods get growing need with the development of science, engineering, economy and so on. Inspired by the idea of Hooke and Jeeves, we introduced an integer m in the algorithm which controls the number of steps of iteration update. We mean along the descent direction to allow the algorithm to?go ahead m steps at most to explore whether we can get better solution further. The experiment proved the strategy’s efficiency. 展开更多
关键词 UNCONSTRAINED OPTIMIZATION derivative-free OPTIMIZATION Pattern SEARCH methods POSITIVE BASES
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AN AFFINE SCALING DERIVATIVE-FREE TRUST REGION METHOD WITH INTERIOR BACKTRACKING TECHNIQUE FOR BOUNDED-CONSTRAINED NONLINEAR PROGRAMMING 被引量:1
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作者 GAO Jing ZHU Detong 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2014年第3期537-564,共28页
This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such ... This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm. 展开更多
关键词 Affine scaling backtracking technique box constrains derivative-free optimization non-linear programming trust region method.
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Automatic Simulation of the Chemical Langevin Equation
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作者 Silvana Ilie Monjur Morshed 《Applied Mathematics》 2013年第1期235-241,共7页
Biochemical systems have important practical applications, in particular to understanding critical intra-cellular processes. Often biochemical kinetic models represent cellular processes as systems of chemical reactio... Biochemical systems have important practical applications, in particular to understanding critical intra-cellular processes. Often biochemical kinetic models represent cellular processes as systems of chemical reactions, traditionally modeled by the deterministic reaction rate equations. In the cellular environment, many biological processes are inherently stochastic. The stochastic fluctuations due to the presence of some low molecular populations may have a great impact on the biochemical system behavior. Then, stochastic models are required for an accurate description of the system dynamics. An important stochastic model of biochemical kinetics is the Chemical Langevin Equation. In this work, we provide a numerical method for approximating the solution of the Chemical Langevin Equation, namely the derivative-free Milstein scheme. The method is compared with the widely used strategy for this class of problems, the Milstein method. As opposed to the Milstein scheme, the proposed strategy has the advantage that it does not require the calculation of exact derivatives, while having the same strong order of accuracy as the Milstein scheme. Therefore it may be used for an automatic simulation of the numerical solution of the Chemical Langevin Equation. The tests on several models of practical interest show that our method performs very well. 展开更多
关键词 Stochastic BIOCHEMICAL KINETICS CHEMICAL LANGEVIN EQUATION derivative-free Milstein method
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A GLOBALLY DERIVTIVE-FREE DESCENT METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS 被引量:2
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作者 Hou-duo Qi (Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China) Yu-zhong Zhang (Institute of Operation Research, QuFu Normal Univer 《Journal of Computational Mathematics》 SCIE CSCD 2000年第3期251-264,共14页
Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for shor... Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free de- scent method in monotone case. We show its global convergence under some mild conditions. If F, the function involved in NCP, is Ro-function, the optimization problem has bounded level sets. A local property of the merit function is discussed. Finally, we report some numerical results. 展开更多
关键词 Complementarity problem NCP-function unconstrained minimization method derivative-free descent method
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