Sums of Squares Polynomial Program Reformulations for Adjustable Robust Linear Optimization Problems with Separable Polynomial Decision Rules

Abstract We show that adjustable robust linear programs with affinely box data uncertainties under separable polynomial decision rules admit exact sums of squares (SOS) reformulations. These problems share the same optimal values and a one-to-one correspondence between solutions. A sum representation non-negativity non-convex over plays key role in reformulation. This reformulation allows us to find solutions uncertain uncertainty by numerically solving their associated equivalent SOS optimization problem using semi-definite programming. illustrate how quality solution improves as degree increases. Our results demonstrate approach actual increases from one fifteen.