[WIP] Add tolerance constructor to approximation configs by acostarelli · Pull Request #105 · Sienna-Platform/InfrastructureOptimizationModels.jl

acostarelli · 2026-05-28T00:26:34Z

TODO:

There are still a few approximations that need to be filled in
Confirm the error bounds with the papers
The constructors are kinda ugly now

… configs Users can now build a config from an error tolerance instead of inverting the method's error formula by hand. Each config with a documented closed-form gap gets a keyword-only outer constructor that takes `tolerance` and `max_delta` (plus `max_delta_x`/`max_delta_y` for bilinear), resolves `depth`, and delegates to the existing positional constructor. Bin2 and HybS get informative error stubs since their composite gap formula isn't documented in-source yet; the no-op configs fall through to Julia's natural MethodError because an empty-struct kw stub would clobber the auto-generated zero-arg constructor. Replaces the four "Relaxation gap <= 2^(...)" tests in test_nmdt_approximations.jl with a new test_tolerance_dispatch.jl that requests several tolerances and asserts achieved gap <= tolerance for each implemented method. Monotonic convergence and structural-correctness tests are retained — only the one-to-one bound checks are replaced. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

github-actions · 2026-05-28T00:33:14Z

Performance Results
Main

This branch

- Move all quadratic and bilinear config constructors inside the struct body as inner constructors using new(...). Quadratic configs take either depth or (tolerance, max_delta) via a single merged kwargs constructor; Bin2Config/HybSConfig keep quad_config positional with kwargs for the remaining fields. Auto-generated all-positional constructors are now suppressed, so every call site moves to kwargs. - Update every positional call site in src/ and test/ accordingly, including internal EpigraphQuadConfig calls in sawtooth.jl, hybs.jl, and nmdt_common.jl, plus the bilinear_delta_benchmark wrappers. - Drop explanatory comments at the top of both no_approx.jl files and the stale "see test_tolerance_dispatch.jl" comment in test_nmdt_approximations.jl. - In test_tolerance_dispatch.jl: rename greek-letter variables to ASCII (eps -> tol, delta), drop the +1e-6 solver-tolerance slack in favor of +1e-10 (pure float-roundoff guard at SOS2 exact-integer boundaries), remove the stub-configs-error-informatively testset, and generalize the non-unit-domain testset to iterate over every config. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

acostarelli

Review 2

Approximation config constructors take only depth/segments now. A new `tol_depth(::Type{Cfg}; tolerance, max_delta, …)::Int` family derives the discrete knob from a target gap. Bilinear configs `Bin2Config{Q}` and `HybSConfig{Q}` are parameterized on their inner quad type so helpers can dispatch on the pair; HybS also exposes `tol_epigraph_depth` for its cross- term knob. Both bilinear helpers restrict to the inner Qs for which the formulation is structurally valid and raise MethodError otherwise. Helper docstrings carry the math derivations (one-sided 2× factor for Bin2 over Sawtooth/SOS2, half-and-half budget split for HybS), so the inversion is auditable from the source. Sawtooth's `epigraph_depth` docstring is corrected: when nonzero it gates a free variable z in [epigraph(x), sawtooth(x)], so the worst-case error becomes `max(Δ²·2^{-2L_s-2}, Δ²·2^{-2L_e-2})` and the epigraph side can dominate when `L_e < L_s`. SOS2 `pwmcc_segments` is documented as an LP- relaxation tightener that does not enter the PWL error bound. Tests cover analytical worst-case points plus a dense grid and log `max_gap / tolerance` per case; ratios stay ≤ 1 across the suite. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

acostarelli

Review 5/29 1

- rename tol_depth → tolerance_depth, tol_epigraph_depth → tolerance_epigraph_depth - share _ceil_positive(x::Float64) helper in quadratic common.jl - generalize _normed_variable! to accept any AbstractJuMPScalar (AffExpr too) - extend Bin2Config{Q} tolerance_depth to support NMDTQuadConfig / DNMDTQuadConfig inner Qs (require epigraph_depth = 0); rewrite bin2 math/notation - rewrite hybs.jl docstring: explain why Q must over-estimate, derive lower/upper from the sandwich inequalities, drop the "budget" wording - state the epigraph_depth ∈ {0} ∪ [depth, ∞) contract in Sawtooth/NMDT/DNMDT tolerance_depth docstrings; add tolerance_epigraph_depth helpers; clarify in struct docstrings that epigraph_depth is a structural MIP change, contrasted with the LP-only pwmcc_segments - drop pwmcc_segments = 0 overrides from tolerance/quadratic tests (no effect on MIP optimum) - split NMDT tightening test into named with/without-tightening cases - test_tolerance_dispatch: multiple dispatch over the if/elseif sampler, include boundary corner points, assert ratio ≤ 1, Δ = 4 → Δ = 7 for SolverSOS2, rename shadowing loop vars, drop @test_throws MethodError testsets Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

acostarelli · 2026-05-29T17:14:59Z

+from `xy` under MIN/MAX objectives.
+
+**Caveat for NMDT/DNMDT inner Q**: these are only one-sided-over when their
+`epigraph_depth = 0`. With `epigraph_depth > 0`, the inner result becomes free


Is this true that they are one-sided when epi_depth=0? I don't agree intuitively. And if this is true, shouldn't this mean we can use this with HybS?

acostarelli · 2026-05-29T17:19:55Z

+in the lower bound and sign `+` in the upper bound, so if `z_x` could
+*under*-estimate `x²` then the `−z_x` term in the lower can drive `lower > xy`
+and the sandwich is invalid. This rules out `EpigraphQuadConfig` (one-sided
+under) and the two-sided `NMDTQuadConfig` / `DNMDTQuadConfig` for the tolerance


So are they one sided or two sided, the nmdt quads?

acostarelli · 2026-05-29T17:24:59Z

+# --- Tolerance helpers ---
+#
+# Notation: Δx, Δy are domain lengths; ε denotes errors. Let
+#   ε_q = max(x² − z_x, y² − z_y, 0)     inner-quad one-sided-over error


If $z_x$ is an over-error, then isn't $\epsilon_q$ forced to be 0?

Replace your math explanation with mine:

Since $z_x$ is an over-estimation of $x^2$, let $\epsilon_x=x^2-z_x$ represent the maximum error in the domain of $x$ . Then, compute the bounds of $z$, our approximation. The lower bound is Bin2:

$\frac{1}{2}(z_x+z_y-z_{p1})$
$\frac{1}{2}(z_p-z_x-z_y)$
$\frac{1}{2}((x+y)^2-\epsilon_{p1}-x^2-\epsilon_x-y^2-\epsilon_y)$
$\frac{1}{2}((x+y^2)-x^2-y^2)-\frac{1}{2}(\epsilon_{p1}+\epsilon_x+\epsilon_y)$
$xy-\frac{1}{2}(\epsilon_{p1}+\epsilon_x+\epsilon_y)$

We are using the same approximation for both inner quadratics, and the same for both $p$ terms, so let $\epsilon_x=\epsilon_y=\epsilon_Q$ and $\epsilon_{p1}=\epsilon_{p2}=\epsilon_E$. Further simplifying above we arrive at $xy-\frac{\epsilon_E}{2}-\epsilon_Q$. A similar computation with the Bin3 upper bound reveals $|z-xy|\le\frac{\epsilon_E}{2}+\epsilon_Q$. If our desired tolerance is $\tau$, we can achieve this with $\epsilon_E=\tau$ and $\epsilon_Q=\frac{\tau}{2}$, arbitrarily.

The other docstrings should be notationally consistent with what I've used here, if not already.

And also, if you can modify the other docstrings to approach a similar proof style as I've done, do that too.

acostarelli · 2026-05-29T19:02:52Z

+Defined for one-sided-over inner quads: `SawtoothQuadConfig`, `SolverSOS2QuadConfig`,
+`ManualSOS2QuadConfig`, `NMDTQuadConfig`, `DNMDTQuadConfig`. `EpigraphQuadConfig`
+is excluded — it is one-sided-under, so the sign of `ε_p` flips and the bound
+above no longer applies; an Epigraph inner quad can drive `z` arbitrarily far


Thinking out loud: can we do Bin3 + epigraph?

acostarelli commented May 28, 2026

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