In numerical computations, one of the most strenuous problems is to solve systems of nonlinear equations. It is known that traditional numerical methods such as Newton methods and their variants require differentiabil...
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In numerical computations, one of the most strenuous problems is to solve systems of nonlinear equations. It is known that traditional numerical methods such as Newton methods and their variants require differentiability and/or good initial guess for the solutions. In practice, it will be difficult to get this initial solution and costly in term of the time to compute Jacobian. Therefore, there is a need to develop an algorithm to avoid the requirements of these traditional methods. This study proposes a new hybrid algorithm by incorporating cuckoo search (CS) with particle swarm optimization (PSO), called CSPSO, for solving systems of nonlinear equations. The goal of the hybridization between CS and PSO is to incorporate the best attributes of two algorithms together to structure a good-quality algorithm. One of the disadvantages to CS, it requires a large number of function evaluations to get the optimal solution, and to PSO, it is trapped into local minima. Our proposed hybrid algorithm attempts to overcome the disadvantages of CS and PSO. Computational experiments of nine benchmark systems of nonlinear equations and 28 benchmark functions of CEC 2013 with various dimensions are applied to test the performance of CSPSO. Computational results show that CSPSO outperforms other existing algorithms by obtaining the optimum solutions for most of the systems of nonlinear equations and 28 benchmark functions of CEC 2013, and reveals its efficacy in the comparison with other algorithms in the literature.
This paper mainly aims to study a new nonmonotone line search slackness technique for unconstrained optimization problems and show that it possesses the global convergence without needing condition of convexity. We es...
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This paper mainly aims to study a new nonmonotone line search slackness technique for unconstrained optimization problems and show that it possesses the global convergence without needing condition of convexity. We establish the corresponding algorithm and illustrate its effectiveness by virtue of some numerical tests. Simulation results indicate that the proposed method is very effective for non-convex functions.
In supervised learning, the Universum, a third class that is not a part of either class in the classification task, has proven to be useful. In this study we propose (NUTBSVM), a Newton based approach for solving in t...
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In supervised learning, the Universum, a third class that is not a part of either class in the classification task, has proven to be useful. In this study we propose (NUTBSVM), a Newton based approach for solving in the primal space the optimizationproblems related to Twin Bounded Support Vector Machines with Universum data (UTBSVM). In the NUTBSVM, the constrained programming problems of UTBSVM are converted into unconstrained optimization problems, and a generalization of Newton's method for solving the unconstrainedproblems is introduced. Numerical experiments on synthetic, UCI, and NDC data sets show the ability and effectiveness of the proposed NUTBSVM. We apply the suggested method for gender detection from face images, and compare it with other methods.
Since the Nash game concept links several optimizationproblems in the Nash game, then the theory for the optimizationproblems can not solve the Nash game directly. Using the regularized Ky-Fan function, we get an un...
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Since the Nash game concept links several optimizationproblems in the Nash game, then the theory for the optimizationproblems can not solve the Nash game directly. Using the regularized Ky-Fan function, we get an unconstrainedoptimization reformulation for the Nash game in the sense that the solution set of the unconstrainedoptimization reformulation is the solution set of the Nash game.
For periodic gait optimizationproblem of bipedal walking robot, based on discrete mechanics and optimal control (DMOC), a class of smoothing penalty function method is proposed. The optimal control strategy and traje...
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For periodic gait optimizationproblem of bipedal walking robot, based on discrete mechanics and optimal control (DMOC), a class of smoothing penalty function method is proposed. The optimal control strategy and trajectory are solved by a new smoothing exact penalty function algorithm. The algorithm Can quickly converge to a stable gait cycle independent, the selection of the initial gait, otherwise, the algorithm only needs one step correction and then generate a stable gait cycle. Numerical simulation results Show that the algorithm is feasible and effective. The algorithm makes the bipedal robot walk efficiently and stably on the even terrain. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. A modified conjugate gradient method is proposed in this paper for unconstrainedoptimization proble...
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ISBN:
(纸本)9781467316842;9781467346856
In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. A modified conjugate gradient method is proposed in this paper for unconstrained optimization problems. The direction of the proposed method provides a descent direction for the objective function. Under mild conditions, we prove that the method with strong Wolfe line search is globally convergent.
Fuzzy nonlinear equation (FNLE) plays an important role in many fields, including mathematics, engineering, statistics and so on. How to solve its numerical solution is an interesting problem. A hybrid conjugate gradi...
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ISBN:
(纸本)9781424473281
Fuzzy nonlinear equation (FNLE) plays an important role in many fields, including mathematics, engineering, statistics and so on. How to solve its numerical solution is an interesting problem. A hybrid conjugate gradient algorithm (HCGA) was proposed for solving FNLE. First, the parametric form of the equation was translated into an equivalent unconstrained optimization problem (UOP). Then, HCGA was applied to solve the corresponding optimizationproblem. Convergence of the algorithm was proved. Finally, numerical examples were given to illustrate the efficencies of HCGA. The comparative study shows that HCGA for solving FNLE is superior to the existent steepest descent algorithm (SDA) in terms of convergence and the numbers of iteration.
Compare to the sequential Broyden method, an asynchronous parallel Broyden method is presented in the paper. We suppose that we have p+q processors, which are divided into two groups. And the first group has p process...
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ISBN:
(纸本)9780878492237
Compare to the sequential Broyden method, an asynchronous parallel Broyden method is presented in the paper. We suppose that we have p+q processors, which are divided into two groups. And the first group has p processors, the second processors has g processors, while the two groups are asynchronous parallel. If we assume that the objective function is twice continuously differentiable and uniformly convex, the global convergence of the algorithm is given. And under the same conditions, we show that the parallel Broyden method is superlinearly convergent.
It is well-known that the Dai-Yuan conjugate gradient method. Recently, Zhang developed two modified Dai-Yuan (MDY) methods that are globally convergence if the standard Armijo line search is used. In this paper, firs...
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ISBN:
(纸本)9781467355322
It is well-known that the Dai-Yuan conjugate gradient method. Recently, Zhang developed two modified Dai-Yuan (MDY) methods that are globally convergence if the standard Armijo line search is used. In this paper, firstly, we investigate the R-convergence rate of the MDY method with inexact Armijo line search. Secondly, We show another MVDY method convergence globally for nonconvex minimization problems. Thirdly, the MVDY method also have R- convergence rate with inexact Armijo line search. Numerical results show that this algorithm is effective in unconstrained optimization problems.
We survey the development of algorithms and theory for the unconstrained optimization problem during the years 1967-1970. Therefore (except for one remark) the material is taken from papers that have already been publ...
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