Multi-Stage Sparse Resource Allocation for Control of Spreading Processes over Networks

The paper’s core convexification idea—splitting 1 − hδ into (1 − hΔ) + h(Δ − δ) and mapping the DP inequalities pk ≥ C + α pk+1 Ak into log-sum-exp constraints via y = log p and logarithmic resource transforms—is sound and matches Proposition 2’s sketch. However, the stated convex program contains serious typographical/semantic errors: (i) bounds (23)–(24) incorrectly use 1 − δ instead of Δ − δ and omit the reference bars, and (ii) the persistence relations “βk = β1 − Σ u” and “δk = δ1 − Σ v” are dimensionally wrong; the correct relations are multiplicative, βk = β̄k e−u/w and Δ − δk = (Δ − δ̄k) e−v/w. These mistakes make the written statement incomplete as an exact equivalence. The candidate solution corrects these issues, proves both directions, and establishes convexity carefully. See the paper’s DP relaxation and LSE constraints (equations (7)–(8), (20)–(21)) and Proposition 2 statement for the intended result, and note the problematic lines in the proposition as printed .