The Symmetric Rank One Formula and its Application in Discrete Nonlinear Optimization

Abstract

The Symmetric Rank One (SR1) update formula is studied for its use in numerically accumulating second order derivative information for optimization. The unique advantage of the SR1 formula is that it does not require specific search directions for development of the Hessian matrix. This is an attractive feature for optimization applications where arbitrary search directions may be necessary. This paper explores the use of the SR1 formula within a procedure based on recursive quadratic programming (RQP) for solving a class of mixed discrete constrained nonlinear programming (MDCNP) problems. Theoretical considerations are presented along with numerical examples which illustrate the procedure and the utility of SR1.