Risk-Constrained Nonconvex Dynamic Resource Allocation has Zero Duality Gap

Dionysios S. Kalogerias

Abstract: We show that risk-constrained dynamic resource allocation problems with general integrable nonconvex instantaneous service functions exhibit zero duality gap. We consider risk constraints which involve convex and positively homogeneous risk measures admitting dual representations with bounded risk envelopes, strictly generalizing expectations. Beyond expectations, particular risk measures supported within our setting include the conditional value-at-risk, the mean-absolute deviation (including the non-monotone case), certain distributionally robust representations and more generally all real-valued coherent risk measures on the space ${\cal L}_{1}$. Our proof technique relies on risk duality in tandem with Uhl's weak extension of Lyapunov's convexity theorem for vector measures taking values in general Banach spaces.