Efficient method for solving one norm equality constrained problem

Abstract

The paper proposes an efficient method for solving a one norm equality constrained optimization problem. In fact, this kind of optimization problems is nonconvex. First, the problem is formulated as the least absolute shrinkage and selection operator (LASSO) optimization problem. Then, it is solved by iterative shrinkage algorithms such as the fast iterative shrinkage thresholding algorithm (FISTA). Next, the solution of the LASSO optimization problem is employed for formulating the constraint of the corresponding least squares constrained optimization problem. The solution of the least squares constrained optimization problem is taken as a near globally optimal solution of the one norm equality constrained optimization problem. Computer numerical simulation results show that our proposed method outperforms existing methods in terms of the accuracy of the obtained solution satisfying the one norm equality constraint.