Bounds-constrained polynomial approximation using the Bernstein basis

A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. much harder version under recent consideration to enforce bounds constraints on the polynomial. In this paper, we consider of constructioning such approximations using polynomials Bernstein basis. We a family inequality-constrained quadratic programs. univariate case, cone constraint allows us search over all nonnegative given degree. both multivariate cases, approximate problems with linear inequality constraints. Additionally, our method can be modified slightly include equality as mass preservation.