---
title: "algorithm-frank-wolfe-tests — Mova code model"
description: "Mova code model of algorithms/src/frank_wolfe/tests.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/algorithms/src/frank_wolfe/tests.rs.groupant/"
---
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# algorithm-frank-wolfe-tests

The groupant beside algorithms/src/frank_wolfe/tests.rs 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

- **kind:** groupant
- **status:** partial descriptive instance
- **source:** [`algorithms/src/frank_wolfe/tests.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/frank_wolfe/tests.rs)
- **source SHA-256:** `fdfe79fad94755e6…`
- **repository folder:** [`algorithms/src/frank_wolfe/tests.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/frank_wolfe/tests.rs.groupant)
- **repository commit:** `855da7bd4a7b`

> **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 | [approximant](#approximant) |
| **ast** | partial | `syntax.json` |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [approximant](#approximant) |
| **tests** | finite checks | [tests](#tests) |

## 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 |
|---|---|---|---|
| `behavior_complement` | behavior_complement | partial relational specification | [behavior_complement](#behavior-complement) |
| `reverse_reconstruction` | reverse_reconstruction | partial relational specification | [reverse_reconstruction](#reverse-reconstruction) |
| `independent_oracle` | independent_oracle | partial relational specification | [independent_oracle](#independent-oracle) |
| `mutation_sensitivity` | mutation_sensitivity | partial relational specification | [mutation_sensitivity](#mutation-sensitivity) |
| `boundary_partition` | boundary_partition | partial relational specification | [boundary_partition](#boundary-partition) |

## Model text


### descriptant

#### frank_wolfe finite checks

The test harness observes finite assertions on frank_wolfe. Analytic formulas and finite grid competitors are distinct forms of evidence; the grid alone proves no optimizer bound.

##### Prospective epoch

The prospective model was saved before source creation in the external wave20 optimization run and retained in prospective.md. Original standard-library Rust, no downloaded solution code.

##### Observations retained

Nine two-coordinate analytic optimizers; zero-curvature linear problem with tied best vertices; dense quadratic against 101 simplex-grid objectives; budget zero and malformed simplex rejection.

##### Limits

Computed max(gap,0)<=tolerance precedes budget exhaustion. Negative roundoff gap is clamped, not treated as a rigorous certificate. If no coordinate changes at an attempted step return Stagnated with iterations incremented; value/gap still describe the unchanged point. No timing or universal machine-accuracy claim.

Reference: Frank and Wolfe, An algorithm for quadratic programming, Naval Research Logistics Quarterly 3 (1956), 95-110.

### model

#### Mathematical combiner

Inputs are the authoritative tests.rs, source-bound partial syntax, forward relation, typed complement first and reverse reconstruction second, specialized relations and named finite evidence. Intersect the accepted-domain relation with each update relation, then partition termination by convergence, budget, stagnation or error. Minimize .5*x'Q*x-b'x on the unit simplex, using the shared conservative symmetric diagonally dominant PSD domain. Choose earliest argmin_i gradient_i, vertex s=e_i and direction d=s-x. Compute gap=-g'd and curvature=d'Qd. If curvature>0 use alpha=min(1,gap/curvature), otherwise alpha=1. Update by the convex combination (1-alpha)*x+alpha*s.

Tests are sibling source nodes; manifest children are absent because these compact files have no independent nested fragment contracts. Syntax does not expand macros or prove semantics.

Retained observation: Nine two-coordinate analytic optimizers; zero-curvature linear problem with tied best vertices; dense quadratic against 101 simplex-grid objectives; budget zero and malformed simplex rejection.

Composition limits: Three checked length-n vectors, shared allocation failures retained. No callback. Fixed matrix/coordinate traversal and earliest gradient ties. No simplex_projection allocation: the linear simplex oracle and convex combination are the method's substantive updates. Computed max(gap,0)<=tolerance precedes budget exhaustion. Negative roundoff gap is clamped, not treated as a rigorous certificate. If no coordinate changes at an attempted step return Stagnated with iterations incremented; value/gap still describe the unchanged point.

### approximant

#### Forward approximant and invariant

The test harness observes finite assertions on frank_wolfe. Analytic formulas and finite grid competitors are distinct forms of evidence; the grid alone proves no optimizer bound.

##### Domain and invariant

Shared validation checks n<=64, matrix shape, finite bounds, symmetry and conservative dominance before simplex feasibility. Initial coordinates nonnegative, mass within 64*n*EPSILON of one. Reject nonfinite value/gradient/gap/curvature/update, negative computed curvature, or excessive updated mass residual. Near-feasible initial input remains near-feasible rather than exactly normalized.

For Q=2I,b=[b0,0], write x=[t,1-t]; independent scalar minimizer t=clip((2+b0)/4,0,1). A linear objective selects earliest best vertex. Dense grid comparisons are finite lower-quality competitors, not a global accuracy proof.

##### Cost

O(n²) validation and O(k*n²) arithmetic, O(n) scratch (x,gradient,direction), n<=64. Harness repeats only the named bounded fixture set; no production throughput claim.

##### Executable approximation gap

No useful percentage-bounded cheaper surrogate is attached. A sampled decrease, projected step, bracket width or KKT/dual residual is not a universal relative objective/solution certificate. No 1/2/5/10% claim is inferred from finite success; zero-reference relative error is undefined without a separately specified metric. This gap is explicit rather than wrapping the exact implementation.

Reference: Frank and Wolfe, An algorithm for quadratic programming, Naval Research Logistics Quarterly 3 (1956), 95-110.

### models

## Typed obernant family

These are scoped partial relations, not executable inverses or semantic proofs.

### behavior_complement

The observation suite excludes the named wrong coefficients, vertices, brackets and statuses on these fixtures: Nine two-coordinate analytic optimizers; zero-curvature linear problem with tied best vertices; dense quadratic against 101 simplex-grid objectives; budget zero and malformed simplex rejection.. It says nothing about callbacks or matrices outside these finite cases; arbitrary unseen bugs remain compatible with all passes.

### reverse_reconstruction

A passing transcript reconstructs only a family of implementations agreeing on these assertions. The analytic oracle is For Q=2I,b=[b0,0], write x=[t,1-t]; independent scalar minimizer t=clip((2+b0)/4,0,1). A linear objective selects earliest best vertex. Dense grid comparisons are finite lower-quality competitors, not a global accuracy proof.. Many different update orders or untested behaviors have the same pass transcript, so source recovery is not unique.

### independent_oracle

For Q=2I,b=[b0,0], write x=[t,1-t]; independent scalar minimizer t=clip((2+b0)/4,0,1). A linear objective selects earliest best vertex. Dense grid comparisons are finite lower-quality competitors, not a global accuracy proof.

### mutation_sensitivity

Reverse gradient argmin to argmax; linear_vertex_and_tie must fail the compiled vertex assertion.

### boundary_partition

Zero curvature chooses alpha=1, earliest equal gradients choose index zero, zero budget returns current feasible point, invalid mass and negative coordinates fail validation.


### tests

#### Executable checks

Run `cargo test -p mova-algorithms frank_wolfe::tests`.

Nine two-coordinate analytic optimizers; zero-curvature linear problem with tied best vertices; dense quadratic against 101 simplex-grid objectives; budget zero and malformed simplex rejection.

Independent oracle: For Q=2I,b=[b0,0], write x=[t,1-t]; independent scalar minimizer t=clip((2+b0)/4,0,1). A linear objective selects earliest best vertex. Dense grid comparisons are finite lower-quality competitors, not a global accuracy proof.

Compiled negative control: Reverse gradient argmin to argmax; linear_vertex_and_tie must fail the compiled vertex assertion.

No allocator failure injection, all-input proof or benchmark is claimed.

### prospective

#### Prospective optimization model
Before source creation. Brent maintains unimodal bracket and three sampled points; accepts safeguarded parabolic proposals, otherwise golden contraction. O(k) callbacks, O(1) storage. Deterministic callback is assumed; strict unimodality cannot be checked. Armijo shrinks positive alpha by rho until f(alpha)<=f0+c*alpha*slope, slope<0. O(k) callbacks, O(1) space; supplied f0 and slope are caller premises.
Dense quadratics f=.5*x'Qx-b'x use symmetric diagonally dominant nonnegative Q, dimension<=64, finite magnitudes<=1e50. This is a sufficient restricted PSD domain, not arbitrary convex quadratics. PG clips x-g/L into finite bounds with L=max absolute row sum; mapping residual is max |x-clip(x-g/L)|. FW on unit simplex selects earliest minimum gradient vertex, gap=g'(x-s), step=min(1,gap/(d'Qd)); linear curvature uses step 1. O(kn²) time O(n) scratch. These real identities are not floating error guarantees.
Lasso minimizes .5||Ax-y||²+lambda||x||1 by cyclic exact coordinate minimization and residual maintenance, using existing soft threshold kernel. Up to 256 rows and 64 columns. O(kmn) time O(m+n) space. Stop on recomputed KKT max violation. Zero columns set zero. Deterministic ties and iteration orders. All validation precedes work; checked allocation and nonfinite arithmetic explicit; budget<=100000, tolerance positive finite. Each routine distinguishes convergence, budget exhaustion and representational stagnation. No percent objective/solution bound. Expected algorithmic advantage: interpolation avoids golden-only work on smooth functions; cached residual updates avoid recomputing predictions per coordinate. No measured speed claim. Executable approximate surrogate deferred: residual and finite samples lack a justified universal supported percentage metric.
References: Brent, Algorithms for Minimization without Derivatives (1973); Armijo (1966); Nocedal and Wright (2006); Friedman et al., Regularization Paths for Generalized Linear Models via Coordinate Descent (2010); Frank and Wolfe (1956).

### validation

#### Validation epoch 2026-10-30

External receipts: `$MOVA_DATA/runs/octopus-wave20-optimization-2026-10-30`. Two debug and two release library runs each pass 568 tests, including 21 new native tests, with identical sorted test-name/outcome transcripts. Strict all-target algorithms Clippy and focused rustfmt pass.

Five independently compiled production mutants are rejected by named runtime assertions; source bytes restored before the positive rerun. This source's control: Reverse gradient argmin to argmax; linear_vertex_and_tie must fail the compiled vertex assertion.

Fresh syntax projections are generated twice and compared before installing syntax.json. These are partial structural observations, not macro-expanded AST or semantic proofs. No performance or universal <=10% result follows.