Numerical Experiments with Matrices Storage Free BFGS Method for Large Scale Unconstrained Optimization

Abstract

Kami mengaji prestasi berangka bagi suatu kaedah kuasi-Newton yang bebas storan matriks untuk pengoptimuman berskala besar, yang kami panggil kaedah F-BFGS. Kami membandingkan prestasinya dengan kaedah memori terhad BFGS, iaitu kaedah L-BFGS yang dibangunkan oleh Nocedal (1980) dan kaedah kecerunan konjugat. Faedah F-BFGS mempunyai saingan yang inggi disebabkan oleh keperluan storan dan kerja pengiraan yang rendah serta berupaya menyelesaikan masalah berskala besar dengan $10^6$ pembolehubah dengan jayanya sedangkan kaedah lain gagal. Katakunci: Pengoptimuman berskala besar; kaedah bebas storan matriks; kaedah memori terhad; kaedah kecerunan konjugat. We study the numerical performance of a matrices storage free quasi-Newton method for large-scale optimization, which we call the F-BFGS method. We compare its performance with that of the limited memory BFGS, L-BFGS methods developed by Nocedal (1980) and the conjugate gradient methods. The F-BFGS method is very competitive due to its low storage requirement and computational labor and also able to solve large-scale problems with $10^6$ variables successfully while other methods fail. Keywords: Large scale optimization; matrices storage free methods; limited memory methods; conjugate gradient methods.