|BBVSCG||Author||A.G. Buckley, A. Lenir|
|Algorithm||Limited memory quasi-Newton|
|Modeling Languages link|
|Commercial Status||free (ask the authors)|
|Platform||Any machine with a reasonable amount of memory and a Fortran compiler|
|Remarks||BBVSCG subroutine implements the limited memory quasi-Newton method as an extension of CONMIN subroutine of Shanno and Phua.
At the very beginning BBVSCG performs the BFGS update. When all available storage is exhausted, the current BFGS approximation to the inverse of the Hessian matrix is retained as a preconditioning matrix. The algorithm continues by performing preconditioned memoryless quasi-Newton steps, equivalent to the preconditioned conjugate gradient method with exact line search. The memoryless quasi-Newton steps are repeated until the criterion of Powell indicates a restarting.
Numerical comparisons between BBVSCG and some other limited memory quasi-Newton methods are given in J.C. Gilbert and C. Lemarechal, Some numerical experiments with variable-storage quasi-Newton algorithms. Mathematical Programming, vol.45, 1989, pp.407-435.
|References||A.G. Buckley, A. Lenir, QN-like variable storage conjugate gradients. Mathematical Programming, vol.27, 1983, pp.155-175.
A.G. Buckley, A. Lenir, Algorithm 630-BBVSCG: A variable storage algorithm for function minimization, ACM TOMS, vol.11, 1985, pp.103-119.
X.Zou, I.M.Navon, M. Berger, K.H. Phua, T. Schlick, F.X. Le Dimet, Numerical experience with limited memory quasi Newton and truncated Newton methods. SIAM Journal on Optimization, vol.3, no.3, August 1993, pp.582-608.