A Reduced Hessian Method for Large-Scale Constrained Optimization

A REDUCED HESSIAN METHOD FOR LARGE SCALE CONSTRAINED OPTIMIZATION by

We propose a quasi Newton algorithm for solving large optimization problems with nonlinear equality constraints It is designed for problems with few degrees of freedom and is motivated by the need to use sparse matrix factorizations The algorithm incorporates a correction vector that approximates the cross term ZWY pY in order to estimate the curvature in both the range and null spaces of the c...

Numerical Experience with a Reduced Hessian Method for Large Scale Constrained Optimization

We propose a quasi-Newton algorithm for solving large optimization problems with nonlinear equality constraints. It is designed for problems with few degrees of freedom, and is motivated by the need to use sparse matrix factorizations. The algorithm incorporates a correction vector that approximates the cross term Z^WYpy in order to estimate the curvature in both the range and null spaces of th...

Limited-Memory Reduced-Hessian Methods for Large-Scale Unconstrained Optimization

Limited-memory BFGS quasi-Newton methods approximate the Hessian matrix of second derivatives by the sum of a diagonal matrix and a fixed number of rank-one matrices. These methods are particularly effective for large problems in which the approximate Hessian cannot be stored explicitly. It can be shown that the conventional BFGS method accumulates approximate curvature in a sequence of expandi...

An analysis of reduced Hessian methods for constrained optimization

OPTIMIZATION TECHNOLOGY CENTER Argonne National Laboratory and Northwestern University NUMERICAL EXPERIENCE WITH A REDUCED HESSIAN METHOD FOR LARGE SCALE CONSTRAINED OPTIMIZATION by

The reduced Hessian SQP algorithm presented in is developed in this paper into a practical method for large scale optimization The novelty of the algorithm lies in the incorporation of a correction vector that approximates the cross term ZWY pY This improves the stability and robustness of the algorithm without increasing its computational cost The paper studies how to implement the algorithm e...