Algorithm 630
A. Buckley, A. Lenir · ACM Transactions on Mathematical Software · 1985
This routine is designed to find a close approximation to a local minimum of a nonlinear function f(x).Here x is a vector of n variables, that is, x = (x1, x2, . . ., r,), and f is assumed to be smooth, that is, to have at least continuous second derivatives.As with almost all minimization algorithms, there is no attempt made to ensure that the minimum obtained is global. METHODThe algorithm is based on an earlier algorithm, namely, CONMIN, due to Shanno and Phua [6], but offers a fundamental facility which was not available in CONMIN.In the CONMIN code, one could either use a conjugate gradient code if little storage was available, or a quasi-Newton code if there was sufficient storage.BBVSCG offers the user the opportunity to specify the amount of available storage; the code then chooses an appropriate algorithm.What is significant is that, if there is not enough space to run the quasi-Newton part of the algorithm, then this new algorithm will use all of the space that has been allocated to it.If this is more than what is needed to run the conjugate gradient code of CONMIN, as one might often expect to be the case, then the algorithm BBVSCG is such that one can expect a more efficient and rapid convergence to the minimum.This