An Algorithm For Nonlinear L₁ Problem

For nonlinear l1 problembased on the conditions for optimality of the nonlinear l1 problem in [1], we first discuss the descent direction of the objective function F(x) in theory , further more , we study the relation between the optimal solution of nonlinear l1 problem and the optimal solution of some kind of quadratic programming problem with box constrains. Hence, we construct a descent algorithm for nonlinear l1 problem and prove theconvergence of the algorithm.In order to improve the efficiency of the algorithm, we not only correct some defects of the primal-dual interior point algorithm in [4], but also give a modified primal-dual interior point algorithm for convex quadratic programming problem with box constraints. Finally, an example shows that the new descent algorithm fornonlinear l1 problem is effective.