In this paper, using sunny generalized nonexpansive retractions which are different from the metric projection and generalized metric projection in Banach spaces, we present new extragradient and line search algorithm...
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In this paper, using sunny generalized nonexpansive retractions which are different from the metric projection and generalized metric projection in Banach spaces, we present new extragradient and line search algorithms for finding the solution of a J-variational inequality whose constraint set is the common elements of the set of fixed points of a family of generalized nonexpansive mappings and the set of solutions of a pseudomonotone J-equilibrium problem for a J -alpha-inverse-strongly monotone operator in a Banach space. To prove strong convergence of generated iterates in the extragradient method, we introduce a I center dot (au)-Lipschitz-type condition and assume that the equilibrium bifunction satisfies this condition. This condition is unnecessary when the linesearch method is used instead of the extragradient method. Using FMINCON optimization toolbox in MATLAB, we give some numerical examples and compare them with several existence results in literature to illustrate the usability of our results.
We consider solving unconstrained optimization problems by means of two popular globalization techniques: trust-region (TR) algorithms and adaptive regularized framework using cubics (ARC). Both techniques require the...
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We consider solving unconstrained optimization problems by means of two popular globalization techniques: trust-region (TR) algorithms and adaptive regularized framework using cubics (ARC). Both techniques require the solution of a so-called "subproblem" in which a trial step is computed by solving an optimization problem involving an approximation of the objective function, called "the model". The latter is supposed to be adequate in a neighborhood of the current iterate. In this paper, we address an important practical question related with the choice of the norm for defining the neighborhood. More precisely, assuming here that the Hessian B of the model is symmetric positive definite, we propose the use of the so-called "energy norm"-defined by vertical bar vertical bar x vertical bar vertical bar(B) = root x(T) B-x for all x is an element of R-n -in both TR and ARC techniques. We show that the use of this norm induces remarkable relations between the trial step of both methods that can be used to obtain efficient practical algorithms. We furthermore consider the use of truncated Krylov subspace methods to obtain an approximate trial step for large scale optimization. Within the energy norm, we obtain line search algorithms along the Newton direction, with a special backtracking strategy and an acceptability condition in the spirit of TR/ARC methods. The new line search algorithm, derived by ARC, enjoys a worst-case iteration complexity of O(is an element of(-3/2)) We show the good potential of the energy norm on a set of numerical experiments.
The combination of the multiple shooting strategy with the generalized Gauss-Newton algorithm turns out in a recognized method for estimating parameters in ordinary differential equations (ODEs) from noisy discrete ob...
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The combination of the multiple shooting strategy with the generalized Gauss-Newton algorithm turns out in a recognized method for estimating parameters in ordinary differential equations (ODEs) from noisy discrete observations. A key issue for an efficient implementation of this method is the accurate integration of the ODE and the evaluation of the derivatives involved in the optimization algorithm. In this paper, we study the feasibility of the Local linearization (LL) approach for the simultaneous numerical integration of the ODE and the evaluation of such derivatives. This integration approach results in a stable method for the accurate approximation of the derivatives with no more computational cost than that involved in the integration of the ODE. The numerical simulations show that the proposed Multiple Shooting-Local linearization method recovers the true parameters value under different scenarios of noisy data. (C) 2016 Elsevier B.V. All rights reserved.
The effect of friction and strain state in upset deformation on deformed texture was investigated by crystal plasticity finite element method. It was observed that around 60% among random initial texture evolves to w...
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The effect of friction and strain state in upset deformation on deformed texture was investigated by crystal plasticity finite element method. It was observed that around 60% among random initial texture evolves to < 111 > within 10 degrees of the upset axis(ND) by 80% upset near the quasi-uniaxial regions, while smearing of this texture components was predicted near the shear dominant regions. Texture intensity plot was introduced to quantitatively investigate the distributions of deformed textures. In addition, a simple Schmid analysis was also performed to explain the origin of strong ND parallel to < 111 > and ND parallel to < 100 > textures from randomly distributed grains.
This paper proposes a linesearch technique to satisfy a relaxed form of the strong Wolfe conditions in order to guarantee the descent condition at each iteration of the Polak-Ribiere-Polyak conjugate gradient algorit...
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This paper proposes a linesearch technique to satisfy a relaxed form of the strong Wolfe conditions in order to guarantee the descent condition at each iteration of the Polak-Ribiere-Polyak conjugate gradient algorithm. It is proved that this line search algorithm preserves the usual convergence properties of any descent algorithm. In particular, it is shown that the Zoutendijk condition holds under mild assumptions. It is also proved that the resulting conjugate gradient algorithm is convergent under a strong convexity assumption. For the nonconvex case, a globally convergent modification is proposed. Numerical tests are presented.
Particle swarm optimization, a new good swarm intelligence paradigm, has been successfully applied to many non-linear optimization problems. In a swarm each particle adjusts its flying toward a promising area dependin...
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ISBN:
(纸本)0780385667
Particle swarm optimization, a new good swarm intelligence paradigm, has been successfully applied to many non-linear optimization problems. In a swarm each particle adjusts its flying toward a promising area depending on cooperative interaction with others. The cooperative interaction of particles provides effective ways to determine the right flying direction for every particle, which is the key reason for the success of PSO. However, previous PSO algorithms are not good at choosing the step-size along the promising direction. In this paper a linesearch method is employed to enhance particle swarm optimizer so that the step size is chosen rationally. The experimental results show that PSO with linesearch method has a potential to achieve better solutions.
A numerical method for finding the roots of any function is developed. This method considers a circle using the concept of curvature instead of the tangential line in the Newton-Raphson method. The compared results be...
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A numerical method for finding the roots of any function is developed. This method considers a circle using the concept of curvature instead of the tangential line in the Newton-Raphson method. The compared results between the proposed method and the Newton-Raphson method are listed. The proposed method has a wider convergent region of initial points and finds more proper solutions than the Newton-Raphson method. In particular, the paper proposes that the curvature method is replaced by the modified Newton method discussed by Ralston in dealing with multiple roots.
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