A new type of preconditioned CG-algorithm with exactly descent condition for solving non-linear unconstrained optimization

Abstract EN

In this paper, a new PCG descent algorithm is proposed using an exact line search to solve a nonlinear unconstrained optimization problem.

The algorithm reduces to a version of the (Anderi N., 2006) conjugate descent algorithm and uses (Oren S.

S., 1974) self-scaling VM-algorithm to solve a large-scale unconstrained optimization problems.

The global convergence of the proposed algorithm has been proved.

Numerical experiments on twenty six well-known test functions with various dimensions are generally encouraging and show that the global convergence of the new proposed algorithm is faster and superior to other similar algorithms in this field.