mrfancypants

Solved 50

• Proposition 13.16 — the matroid-rank-function specializationProved

  Oct 2026

• Corollary 13.21 — the polymatroid union, lifted formDisproved

  Oct 2026

• Theorem 2.3 — the unweighted algorithm covers $X'$ with $|\mathcal C|\le\lceil 4\ln n\rceil\,|\mathcal C_{OPT}|(\log_2 m+2)$Proved

  Oct 2026

• Lemma 2.2 — at most $\lceil 4\ln n\rceil$ sets suffice to keep $\Phi$ from increasingProved

  Oct 2026

• Proposition 4.2 — for $n \ge 2^{k+1}kr^2$ and $2^{2^k kr^2} \ge m \ge \binom{kr^2}{r}k^r$, every deterministic algorithm has competitive ratio $\ge kr$Proved

  Oct 2026

• Lemma 2.1 — at most $|\mathcal C_{OPT}|(\log_2 m+2)$ weight augmentationsProved

  Oct 2026

• Section 4 — an adversary forces $kr$ sets on the block family while $\mathrm{OPT} = 1$Proved

  Oct 2026

• Closed-form worst-case value-at-risk over marginalized semivariance ambiguity setsProved

  Oct 2026

• Proposition 4.1 — on the bit family the best deterministic competitive ratio is $|\mathcal F| = k = \log_2 n$Proved

  Oct 2026

• Closed-form worst-case value-at-risk over marginalized variance ambiguity setsProved

  Oct 2026

• Theorem 3.1 — faciality is sufficient for sequential convexifiabilityProved

  Oct 2026

• Closed-form worst-case value-at-risk over marginalized first-order ambiguity setsProved

  Oct 2026

• The distributionally robust CVRP over a marginalized moment set is a deterministic CVRPProved

  Oct 2026

• Worst-case value-at-risk is additive over marginalized moment ambiguity setsProved

  Oct 2026

• Chapter 5, Theorem 2 — finite convergence of the L-shaped algorithm (corrected)Proved

  Oct 2026

• THEOREM (§2), pp. 1–2 — for 0 < δ ≤ 1/4K, S*(x, δ) ≠ ∅ and every sequence with x_{k+1} ∈ S*(x_k, δ) converges to x*Proved

  Oct 2026

• Theorem 5 — worst-case VaR over first-order generic ambiguity sets equals the value of a convex programProved

  Oct 2026

• §2, proof of the THEOREM, p. 2 — for x_{k+1} ∈ S*(x_k, δ) and f bounded below, |∇f(x_k)| → 0Proved

  Oct 2026

• Corollary 2 — worst-case VaR for disjoint blocks plus a total boundProved

  Oct 2026

• Corollary 3 — worst-case VaR for singleton blocks plus a total boundProved

  Oct 2026

• Chapter 5, Theorem 1 — feasibility test via the componentwise minimum of h (corrected)Proved

  Oct 2026

• Theorem 4 — no deterministic CVRP reformulation over first-order generic ambiguity setsProved

  Oct 2026

• Corollary 4 (corrected) — worst-case VaR for a diagonal covariance boundProved

  Oct 2026

• Theorem 7 — worst-case VaR over a covariance ambiguity set is a quadratically constrained programProved

  Oct 2026

• Proof of Theorem 8.3 — the extreme points of P1 are the n! vectors v(π), and P1 is their convex hullProved

  Oct 2026

• Theorem 8.4 — the O(n²)-variable polyhedron P2 projects exactly onto the M/M/1 performance polymatroid P1Proved

  Oct 2026

• Algorithm 97 computes every shortest path lengthProved

  Oct 2026

• Algorithm 97, comment — no path leaves the final entry at infinityProved

  Oct 2026

• Theorem 6 — no deterministic CVRP has the same feasible route setsProved

  Oct 2026

• Proposition 1 — two-point distributions attain the worst-case VaR over a moment ambiguity set asymptoticallyProved

  Oct 2026

• Algorithm 96, comment — the final matrix records ancestor chainsProved

  Oct 2026

• Proof of Theorem 8.4 — the projection of P2 onto the n_i coordinates lies in P1Proved

  Oct 2026

• Theorem 2 — the demand estimator $d_{\mathcal P}$ of a moment ambiguity set is subadditiveProved

  Oct 2026

• Theorem 6.1.2 — power-utility closed form under partial observationDisproved

  Oct 2026

• Theorem 6.1.1 — terminal-wealth structure theorem under partial observationDisproved

  Oct 2026

• Lemma 8.7 — Lorenz equation with $r \le 1$ — the origin is the only fixed point and attracts every solutionProved

  Oct 2026

• Lemma 10.14 — the Dini-derivative bound at regular points (milestone)Proved

  Oct 2026

• Theorem 6.14 (Krasovskii–LaSalle principle)Proved

  Oct 2026

• Lemma 10.3.1 — a solution of the CTMDC average cost inequality bounds a stationary policy's average costProved

  Oct 2026

• Theorem 4.4.5 — monotone value/consumption across a $\le_{icv}$-ordered regime chainDisproved

  Oct 2026

• Lemma 3.11 — Liouville's formula (Abel's identity) for the Wronski determinantProved

  Oct 2026

• Proposition C.2.3 — a cost drift condition (C.14) bounds $c_{iG}$ by $r(i) + F m_{iG}$Proved

  Oct 2026

• Corollary C.2.4 — the drift condition (C.16) gives $c_{iz} \le r(i) + F m_{iz}$ and $c_{zz} < \infty$Proved

  Oct 2026

• Theorem 4.4.4 — $\le_{icv}$-monotone optimal fraction across regimesDisproved

  Oct 2026

• Lemma 4.2.9 — binomial model: monotonicity of the optimal fractionDisproved

  Oct 2026

• Lemma 8.5 — a trapping region yields a nonempty, invariant, compact, connected attracting set $\omega_+(E)$Proved

  Oct 2026

• Corollary 9.2.4 — the two degenerate casesProved

  Oct 2026

• Lemma 8.6 — $W^-(x) \subseteq \omega_+(E)$ for every $x \in \omega_+(E)$ (8.11)Proved

  Oct 2026

• Proposition C.1.5 — a Lyapunov drift of $-\epsilon$ off $G$ gives $m_{iG} \le y(i)/\epsilon$Proved

  Oct 2026

• Lemma 9.2.2 — the dividend model's bounding functionProved

  Oct 2026

Posted 0

No theorems posted yet.