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Conjugate gradient algorithms for conic functions

Ladislav Lukšan (1986)

Aplikace matematiky

The paper contains a description and an analysis of two modifications of the conjugate gradient method for unconstrained minimization which find a minimum of the conic function after a finite number of steps. Moreover, further extension of the conjugate gradient method is given which is based on a more general class of the model functions.

Convergence analysis of adaptive trust region methods

Zhen-Jun Shi, Xiang-Sun Zhang, Jie Shen (2007)

RAIRO - Operations Research

In this paper, we propose a new class of adaptive trust region methods for unconstrained optimization problems and develop some convergence properties. In the new algorithms, we use the current iterative information to define a suitable initial trust region radius at each iteration. The initial trust region radius is more reasonable in the sense that the trust region model and the objective function are more consistent at the current iterate. The global convergence, super-linear and quadratic convergence...

Differential evolution algorithm combined with chaotic pattern search

Yaoyao He, Jianzhong Zhou, Ning Lu, Hui Qin, Youlin Lu (2010)

Kybernetika

Differential evolution algorithm combined with chaotic pattern search(DE-CPS) for global optimization is introduced to improve the performance of simple DE algorithm. Pattern search algorithm using chaotic variables instead of random variables is used to accelerate the convergence of solving the objective value. Experiments on 6 benchmark problems, including morbid Rosenbrock function, show that the novel hybrid algorithm is effective for nonlinear optimization problems in high dimensional space....

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