A quasi-Newton based pattern search algorithm for unconstrained optimization
The authors study the general unconstrained optimization problem where the objective function is a continuously differentiable function. It improves upon the classic BFGS (Broyden, Fletcher, Goldfard, Shanno) algorithm, by combining this technique with pattern search. In particular, the conjugate factorization of approximating Hessian matrices of the BFGS scheme are used to produce a series of positive basis for the pattern search. The authors, after presenting the methodological background of the BFGS algorithm and the novelty of their approach in section 2, proceed to study convergence issues (with proof) in section 3. The article concludes with a section containing numerical experimentation and a list of useful references.
scientific article; zbMATH DE number 5125261
scientific article