Abstract: In this paper,we present a superlnear convergence algorithm for nonlinear optimization with linear constraints using matrix decomposition and generalized projection techniques. The algorithm nees not to search the set of δ-active constraints and only needs one computation to the proective matrix at each itertion. Numerical instability of computation is avoided. The algorithm is practical because inexact linear search is adopted and the iterative formula of inverse matrix are given too. The convergence theorem and superlnear convergence rate theorem of the algorithm are proved.

Key words: matrix decomposition, generalized gradient projection, globol conrergence, Superlinear convergence