Superlinear conjugate gradient method with adaptable step length and constant momentum term

First order line search optimization techniques gained essential practical importance over second order optimization techniques due to their computati onal simplicity and low memory requirements. The computational excess of se cond order methods becomes unbearable for large optimization tasks. The onl y applicable optimization techniques in such cases are variations of first order approaches. This article presents one such variation of first order l ine search optimization technique. The presented algorithm has substantiall y simplified a line search subproblem into a single step calculation of the appropriate value of step length. This remarkably simplifies the implement ation and computational complexity of the line search subproblem and yet do es not harm the stability of the method. The algorithm is theoretically pro ven convergent, with superlinear convergence rates, and exactly classified within the formerly proposed classification framework for first order optim ization [1]. Performance of the proposed algorithm is practically evaluated on five data sets and compared to the relevant standard first order optimi zation technique. The results indicate superior performance of the presente d algorithm over the standard first order method.