Quasi-Newton Methods for Solving Nonlinear Programming Problems

Abstract

In the present paper the problem of constrained equality optimization is reduced to sequential solving a series of problems of quadratic programming. The Hessian of the Lagrangian is approximated by a sequence of symmetric positive definite matrices. The matrix approximation is updated at every iteration by a Gram- Schmidt modified algorithm. We establish that methods is locally convergent and the sequence {xk}converges to the solution a two-step superlinear rate.