On secant updates for use in general constrained optimization

A Curvilinear Search Using Tridiagonal Secant Updates for Unconstrained Optimization

Least-change quasi-Newton updates for equality-constrained optimization

January 28, 2000 Abstract. This paper investigates quasi-Newton updates for equality-constrained optimization. Using a least-change argument we derive a class of rank-3 updates to approximations of the one-sided projection of the Hessian of the Lagrangian which keeps the appropriate part symmetric (and possibly positive definite). By imposing the usual assumptions we are able to prove 1-step su...

Direct Secant Updates of Matrix Factorizations

This paper presents a new context for using the sparse Broyden update method to solve systems of nonlinear equations. The setting for this work is that a Newton-like algorithm is assumed to be available which incorporates a workable strategy for improving poor initial guesses and providing a satisfactory Jacobian matrix approximation whenever required. The total cost of obtaining each Jacobian ...

Quasi-Newton updates with weighted secant equations

We provide a formula for variational quasi-Newton updates with multiple weighted secant equations. The derivation of the formula leads to a Sylvester equation in the correction matrix. Examples are given.

Maintaining the positive definiteness of the matrices in reduced secant methods for equality constrained optimization