Parametric linear and quadratic optimization by elimina-tion

We propose a new elimination method for linear and quadratic optimization involving parametric coeecients. In comparison to the classical Fourier-Motzkin method that is of doubly exponential worst-case complexity our method is singly exponential in the worst case. Moreover it applies also to the minimization of a quadratic objective functions without convexity hypothesis under linear constraints, and to objective functions with arbitrary parametric coeecients. For problems with additive parameters the method is worst-case optimal. Examples computed in a REDUCE{ implementation connrm the superiority of the method over Fourier-Motzkin and its applicability to problems of interesting size.