Abstract
In this paper, we present a new conjugate gradient method, in which the search direction is computed by minimizing a selected approximate model in a two-dimensional subspace. That is, if the objective function is not close to a quadratic, the search direction is generated by a conic model. Otherwise, a quadratic model is considered. The direction of the proposed method is proved to possess the sufficient descent property. With the modified nonmonotone line search, we establish a global convergence of the proposed method under appropriate assumptions. R-linear convergence of the proposed method is also analyzed. Numerical results using two different test function collections show that the proposed algorithm is efficient.
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