Bernstein polynomials for PDE constrained optimization problems with L1 norm

In this article, we present a new approach to solve a class of sparse optimization problems. Given the extraordinary ability of Bernstein polynomials to approximate the solution of PDEs, here we use these polynomials to solve sparse PDE constarined optimization problems. For this purpose, we first extract the necessary conditions for the optimality of these problems using the Lagrange muliplier method and then solve these conditions with the help of Bernstein polynomials. Finally, a example is presented to illustrate the ability of proposed approach