Numerical experiments on the methods of dual matrices for function minimization
Chambliss, Joe Preston
Huang, H. Y.
Master of Science
Four algorithms of dual matrices for function minimization introduced in Ref. 1 are tested through several numerical examples. Three quadratic functions and five nonquadratic functions are investigated. For quadratic functions, the results show that the convergence is achieved in at most n+1 iterations, where n is the number of variables. Since one-dimensional search is not needed in these algorithms the total number of gradient evaluations for convergence is at most n+2. This represents a saving on the gradient evaluations versus 2n+1 required by the conventional quadratically convergent algorithms. For nonquadratic functions, the results show that these algorithms are very stable and efficient. Also, the effects of stepsize factor on these algorithms are investigated.