Elamur Groupantsoptimization-solvers
The groupant beside models/optimization-solvers.groupant in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial source model | forward |
| ast | not materialized | |
| composition | partial source model | composition |
| cost | partial source model | cost |
| descriptant | partial source model | epoch-memory |
| invariant | partial source model | invariant |
| tests | bounded executed | checks |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
optimization-solvers-behavior-complement | behavior_complement | partial source model | behavior-complement |
optimization-solvers-reverse-reconstruction | reverse_reconstruction | partial source model | reverse-reconstruction |
optimization-solvers-scalar-stationarity | stationarity_transport | partial source model | scalar-stationarity |
optimization-solvers-diagonal-equations | residual_transport | partial source model | diagonal-equations |
optimization-solvers-conditioning | conditional_error_bound | partial source model | conditioning |
Model text
model
optimization-solvers
forward
Bracket roots and deterministic strictly unimodal minima; descend diagonal quadratics and solve dense symmetric positive definite linear systems with explicit stopping observations.
invariant
Preserve finite reports, bracket order, dimensional agreement and distinct converged, exhausted and stagnated states. True residual is recomputed for stopping.
cost
Sum O(k_b+k_g+nk_d+n^2k_c) arithmetic plus callback costs; serial auxiliary O(n), input matrix O(n^2). Hard dimension and iteration limits remain leaf-specific.
composition
On q(x)=dx^2/2-bx with d>0, derivative root, scalar minimizer, diagonal descent and one-dimensional CG share b/d. For a common diagonal system, GD and CG target identical stationarity but need not share iteration counts or statuses.
epoch-memory
Wave19, 2026-10-30. Models retain real-arithmetic assumptions separately from native finite checks. Kernels are library tools, not automatically adopted into training or inference.
checks
["quadratic_solvers_join_scalar_roots_and_polynomial_values"]
limitations
Continuity, deterministic strict unimodality and global SPD are not established by sampling or visited curvature. Residual magnitude alone does not bound coordinate error without conditioning. Floating-point underflow and conservative arithmetic rejection remain possible.
catalog
Typed family relations
Each relation keeps its own domain and assurance.
behavior-complement
Type: behavior_complement.
Exclude input/report pairs outside each tagged solver relation: exhausted or stagnant reports relabeled as convergence, bracket-width bounds promoted to objective bounds, residual norms promoted to unconditional coordinate error, or visited positive curvature promoted to global SPD.
reverse-reconstruction
Type: reverse_reconstruction.
A returned estimate and status admit many callbacks, brackets, initial states and budgets. For zero residual x, any positive diagonal D with b=D*x is compatible. Common roots/minima survive positive scaling; output does not uniquely recover the problem.
scalar-stationarity
Type: stationarity_transport.
For q(x)=dx^2/2-bx,d>0 with valid enclosing intervals, q'=d*x-b links bisection, golden-section, GD and CG to the same b/d. Native finite fixtures compare additive coordinates with explicit tolerance, not status equality.
diagonal-equations
Type: residual_transport.
For the same positive diagonal D and b, gradient Dx-b and linear residual b-Dx differ only by sign. Their Euclidean norms agree in real arithmetic; rounding and solver trajectories remain separate.
conditioning
Type: conditional_error_bound.
For SPD A with known lambda_min>0, ||x-x*||2 <= ||A*x-b||2/lambda_min in real arithmetic. This group supplies no eigenvalue certificate; without that premise the residual-to-solution bound is absent.
wave19-evidence
Family evidence — 2026-10-30
This family binds eight implementation/test sources through its manifest; views are partial source-derived models. Selected named joins are ["quadratic_solvers_join_scalar_roots_and_polynomial_values"] in algorithms/tests/composition_wave19.rs. Those checks pass four times as part of the 616-check suite. Leaf oracles and compiled production controls remain separately bound in adjacent evidence.
Integrated evidence records receipts; conditional laws outside these fixture scopes are not promoted to executed checks. No joint universal percentage bound follows from family membership.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/models/optimization-solvers.groupant/