Lagrange programming neural network for the l1-norm constrained quadratic minimization

Abstract

The Lagrange programming neural network (LPNN) is a framework for solving constrained nonlinear programm problems. But it can solve differentiable objective/contraint functions only. As the l1-norm constrained quadratic minimization (L1CQM), one of the sparse approximation problems, contains the nondifferentiable constraint, the LPNN cannot be used for solving L1CQM. This paper formulates a new LPNN model, based on introducing hidden states, for solving the L1CQM problem. Besides, we discuss the stability properties of the new LPNN model. Simulation shows that the performance of the LPNN is similar to that of the conventional numerical method.