Quadratic optimization in the problems of active control of sound

By contrast, in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L2 norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L2 minimization is an easy problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we can compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L2 differ drastically from those obtained in the sense of L1.