Refinement of estimates of the convergence rate for the method of random search. (Russian) Zbl 0589.90061

The rate of convergence of a random search method is studied for the problem of minimizing the quadratic form \(f(x)=ax^ 2_ 1+x^ 2_ 2+x^ 2_ 3\), where \(0<a<1\) and the direction is chosen as a realization of a vector uniformly distributed on the surface of the three dimensional unit ball and the step size is found in an optimal way. For small values of a, comparisons of numerical results are given.
Reviewer: J.Dupačova


90C20 Quadratic programming
65K10 Numerical optimization and variational techniques
90C99 Mathematical programming
65K05 Numerical mathematical programming methods
Full Text: EuDML