Universal duality in conic convex optimization

摘要

Given a primal-dual pair of linear programs, it is well known that if their optimal values are viewed as lying on the extended real line, then the duality gap is zero, unless both problems are infeasible, in which case the optimal values are +∞ and ?∞. In contrast, for optimization problems over nonpolyhedral convex cones, a nonzero duality gap can exist when either the primal or the dual is feasible.