# The Use of Linear Programming for the Solution of Sparse Sets of Nonlinear Equations

I. S. Duff, J. Nocedal, J. K. Reid

Research output: Contribution to journalArticlepeer-review

## Abstract

In this paper we propose a trust region algorithm for solving sparse sets of nonlinear equations. It is based on minimizing the $l_1$-norm of the linearized residual vector within an $l_\infty$-norm trust region, thereby permitting linear programming techniques to be easily applied. The new algorithm has sparsity advantages over the Levenberg-Marquardt algorithm.
Original language English 99-108 SIAM Journal on Scientific Computing 8 https://doi.org/10.1137/0908024 Published - 1987