We develop new design procedures for optimizing anti-windup control applicable to open-loop stable multivariable plants subject to input saturations. The optimizing anti-windup control falls into a class of compensator commonly termed directionality compensation. The computation of the control involves the on-line solution of a low-order quadratic program in place of simple saturation. We exploit the equivalence of the quadratic program to a feedthrough term in parallel with a deadzone-like nonlinearity that satisfies a sector bound condition. This allows for LMI-based anti-windup synthesis using a decoupled structure similar to that proposed in the literature for anti-windup schemes with simple saturation. We demonstrate the effectiveness of the design compared to several schemes using a highly ill-conditioned benchmark example.