An Active Set Algorithm for Nonlinear Programming with Linear Constraints

The projected gradient method is an efficient method for solving nonlinear programming problems with linear constraints. However, it cannot maintain the sparsity of the coefficient matrix of linear constraints, which results in lower calculation efficiency. This article presented a new method to solve the problem, by which the author generated the null space of active constraints by applying technique of the implicit LU decomposition of a matrix in the process of determining the feasible direction on feasible points. Numerical test results show that the active set algorithm for nonlinear programming with linear constraints provided in this article can not only maintain the sparsity of coefficient matrix of linear constrains, but also improve the calculation efficiency.