An efficient conjugate directions method without linear minimization

An algorithm of conjugate directions for unconstrained minimization is presented, called Single-Step Conjugate Directions Method (SSCDM) that differs from the known algorithms in the following points: (1) only one step is made on each iteration, without the linear searches of a minimum; (2) each step includes simultaneous displacements along all conjugate directions found on previous steps (instead of consequent steps along each conjugate vector); (3) each new conjugate direction is determined by the general procedure of construction of conjugate vectors, without assumption that minima along the conjugate directions were reached on previous steps. These features of the algorithm eliminate high sensitivity to computation errors pertinent to usual methods of conjugate directions and simultaneously significantly reduce the running time. Performance of the algorithm is demonstrated by applying it to a set of standard test-functions and solving a problem of high-energy physics with a Monte-Carlo-type objective function.