The Use of a Nonquadratic Model in a Conjugate Gradient Method of Optimization with Inexact Line Searches

摘要

Conjugate gradient methods in optimization were studied. The traditional search method exhibits finite termination when applied to quadratic problems if exact line searches are used. The use of these, however, can cause excessive computational effort and consequently conjugate gradient methods, using inexact line searches, are suggested. Using a rational model (nonquadratic), different standard test functions were tried in various dimensions in order to examine the effectiveness of three methods: (1) function minimization by conjugate gradients, i.e., standard method; (2) conjugate gradient optimization method invariant to nonlinear scaling; and (3) conjugate direction method. Numerical results show the performance of the three methods, tested on a variety of updating formulas for the search directions and line search accuracy parameters.