Dynamic scaling on the modified limited memory BFGS updates for unconstrained optimization

This paper deals with the scaling of a modifiedlimited memory BFGS algorithm for solving unconstrainedoptimization problems. The basic idea is to combine a modifiedlimited memory BFGS update and the preconditioning techniqueof equilibrating the inverse Hessian approximations. Enhancedcurvature information about the objective function is stored in theform of a diagonal matrix, and plays the dual role of providing aninitial matrix and of equilibrating for modified limited memoryBFGS (mLBFGS) iterations. Numerical experiments indicate thatthe new algorithm is very effective.