New Hybrid Conjugate Gradient Algorithms for Unconstrained Optimization
نویسنده
چکیده
New hybrid conjugate gradient algorithms are proposed and analyzed. In these hybrid algorithms the famous parameter k β is computed as a convex combination of the Polak-Ribière-Polyak and Dai-Yuan conjugate gradient algorithms. In one hybrid algorithm the parameter in convex combination is computed in such a way that the conjugacy condition is satisfied, independent of the line search. In the other, the parameter in convex combination is computed in such a way that the conjugate gradient direction is the Newton direction. The algorithm uses the standard Wolfe line search conditions. Numerical comparisons with conjugate gradient algorithms using a set of 750 unconstrained optimization problems, some of them from the CUTE library, show that the hybrid computational scheme based on conjugacy condition outperform the known hybrid conjugate gradient algorithms. MSC: 49M07, 49M10, 90C06, 65K
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