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LIT-1975: Adjustable robust solutions of uncertain linear programs

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Properties6
StatusActive — read 2026-11-03 (NOTE-1503), from the published text on A. Nemirovski's faculty page; worth reading as the standard distinction between robust (∃ solution ∀ data) and adjustable robust (∀ data ∃ adjustment) decisions, with information bases between them, which CLAIM-537's conditions I and II instantiate; its own intermediate case is a restriction on the rule's form (affine), not on what is read.
Version2
Tagsoperations-research, mathematics
Cited as “grounds” byCLAIM-537 — In tolerance-bounded compatibility on a graph with disturbed offsets, |Dx − a₀ − w| ≤ δ for |w_e| ≤ η_e, a compatible configuration exists for every disturbance exactly when |cᵀa₀| + Σ η_e|c_e| ≤ Σ δ_e|c_e| on every cycle, and one configuration serves every disturbance exactly when η ≤ δ and |cᵀa₀| ≤ Σ(δ_e − η_e)|c_e|; an agent that chooses its configuration from what it observes needs the second condition within each class of disturbances it cannot tell apart, so whether a compatible state can be selected lies between the two and depends on what the agent can read
Cited as “paper” byNOTE-1503 — Ben-Tal, Goryashko, Guslitzer & Nemirovski — Adjustable robust solutions
Cited as “source” byTHEORY-1303 — For an uncertain linear program, a decision fixed before the data are revealed must satisfy every realization at once (the robust counterpart, ∃ solution ∀ data), while a decision that may adjust after them need only have a feasible adjustment for each (the adjustable robust counterpart, ∀ data ∃ adjustment); the second is never more conservative and can be feasible where the first is not, the two coincide when each constraint's uncertainty is its own, and decisions may be restricted between them by what part of the data they read or by the form of the rule

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Ben-Tal, A., Goryashko, A., Guslitzer, E., & Nemirovski, A. (2004). Adjustable robust solutions of uncertain linear programs. Mathematical Programming, 99(2), 351–376. doi:10.1007/s10107-003-0454-y.

Read on 2026-11-03 (NOTE-1503; THEORY-1303).

Key takeaways

  • RC: ∃v ∀ζ; ARC: ∀ζ ∃v (eqs. 5–6). Equal under constraint-wise uncertainty (Theorem 2.1).
  • Information basis: each decision may read a prescribed part of the data (p. 353); named, used in §5, not developed in general.
  • AARC: adjustments affine in the data, tractable with fixed recourse.
  • Inventory at 20% uncertainty: on-line 34,583, standard 35,121, four-period delay and none infeasible (Table 2).

Standing in the record

The framing of CLAIM-537: a compatible configuration may be chosen after a disturbance, fixed before it, or chosen from what is observed of it. The record’s question there is which of the three an agent’s legibility gives it.

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