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

The groupant beside algorithms/src/brent_minimize/mod.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/brent_minimize/mod.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/brent_minimize/mod.rs)
- **source SHA-256:** `24e5a58a71c362ce…`
- **repository folder:** [`algorithms/src/brent_minimize/mod.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/brent_minimize/mod.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) |
| `update_relation` | update_relation | partial relational specification | [update_relation](#update-relation) |
| `termination_partition` | termination_partition | partial relational specification | [termination_partition](#termination-partition) |
| `finite_arithmetic` | finite_arithmetic | partial relational specification | [finite_arithmetic](#finite-arithmetic) |
| `resource_observation` | resource_observation | partial relational specification | [resource_observation](#resource-observation) |

## Model text


### descriptant

#### brent_minimize implementation

For a deterministic strictly unimodal f on [a,b], retain the sampled best x and two historical samples w,v. A safeguarded interpolating-parabola displacement is accepted only within the bracket and below half the previous displacement; otherwise choose the golden displacement toward the longer side. Comparing f(u) to f(x) removes the opposite interval. Equality promotes u. Strict unimodality is a caller premise, not inferred from samples.

##### 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

17 translated quadratics; absolute-value cusp; monotone endpoint; zero budget and exact callback counts; invalid interval callback not invoked; NaN callback; adjacent floats; repeated exponential fixture.

##### Limits

Width<=tolerance wins over budget exhaustion; budget wins over inability to generate a distinct interior u. A representationally unchanged or exterior candidate yields Stagnated. Endpoint minima are approached by interior samples; value is always one actual sampled value. No timing or universal machine-accuracy claim.

Reference: Brent, Algorithms for Minimization without Derivatives (1973), chapter 5.

### model

#### Mathematical combiner

Inputs are the authoritative mod.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. For a deterministic strictly unimodal f on [a,b], retain the sampled best x and two historical samples w,v. A safeguarded interpolating-parabola displacement is accepted only within the bracket and below half the previous displacement; otherwise choose the golden displacement toward the longer side. Comparing f(u) to f(x) removes the opposite interval. Equality promotes u. Strict unimodality is a caller premise, not inferred from samples.

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: 17 translated quadratics; absolute-value cusp; monotone endpoint; zero budget and exact callback counts; invalid interval callback not invoked; NaN callback; adjacent floats; repeated exponential fixture.

Composition limits: No internal heap allocation. Validate all scalar configuration before the first callback; each completed iteration adds exactly one evaluation. Stateful callbacks are accepted syntactically but deterministic semantics require equal values at equal arguments. Panics and callback allocations are not caught. Width<=tolerance wins over budget exhaustion; budget wins over inability to generate a distinct interior u. A representationally unchanged or exterior candidate yields Stagnated. Endpoint minima are approached by interior samples; value is always one actual sampled value.

### approximant

#### Forward approximant and invariant

For a deterministic strictly unimodal f on [a,b], retain the sampled best x and two historical samples w,v. A safeguarded interpolating-parabola displacement is accepted only within the bracket and below half the previous displacement; otherwise choose the golden displacement toward the longer side. Comparing f(u) to f(x) removes the opposite interval. Equality promotes u. Strict unimodality is a caller premise, not inferred from samples.

##### Domain and invariant

Endpoints are finite, abs<=1e50, left<right; tolerance positive finite, budget<=100000. Reject callback NaN/infinity separately from nonfinite interpolation arithmetic. Minimum step max(tol/8,EPSILON*abs(x)) prevents most repeated samples; tiny tolerance may still stagnate.

The real parabola through (x,fx),(w,fw),(v,fv) supplies p; reject duplicated abscissas, zero denominator, unsafe bracket position or excessive displacement. Fallback is golden*(selected endpoint-x). Promotion shifts v<-w,w<-x,x<-u, so sampled-value associations remain synchronized.

##### Cost

O(k) arithmetic and at most k+1 callback evaluations; O(1) internal storage, callback work excluded. No internal heap allocation. Validate all scalar configuration before the first callback; each completed iteration adds exactly one evaluation. Stateful callbacks are accepted syntactically but deterministic semantics require equal values at equal arguments. Panics and callback allocations are not caught.

##### 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: Brent, Algorithms for Minimization without Derivatives (1973), chapter 5.

### models

## Typed obernant family

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

### behavior_complement

A terminating report with estimate outside [left,right] or evaluations unequal to iterations+1 is outside this relation. The method cannot report a certified relative objective error: arbitrarily narrow unsampled wells can agree with the complete observed transcript while violating unimodality and containing a better minimum.

### reverse_reconstruction

A report restricts input intervals to those containing its retained bracket and callbacks to those realizing its finite sampled values/comparisons. Infinitely many continuous functions interpolate those samples; the original function is not recoverable. Under the separate unimodality premise, compatible minima remain in the retained bracket up to finite arithmetic.

### update_relation

The real parabola through (x,fx),(w,fw),(v,fv) supplies p; reject duplicated abscissas, zero denominator, unsafe bracket position or excessive displacement. Fallback is golden*(selected endpoint-x). Promotion shifts v<-w,w<-x,x<-u, so sampled-value associations remain synchronized.

### termination_partition

Width<=tolerance wins over budget exhaustion; budget wins over inability to generate a distinct interior u. A representationally unchanged or exterior candidate yields Stagnated. Endpoint minima are approached by interior samples; value is always one actual sampled value.

### finite_arithmetic

Endpoints are finite, abs<=1e50, left<right; tolerance positive finite, budget<=100000. Reject callback NaN/infinity separately from nonfinite interpolation arithmetic. Minimum step max(tol/8,EPSILON*abs(x)) prevents most repeated samples; tiny tolerance may still stagnate.

### resource_observation

No internal heap allocation. Validate all scalar configuration before the first callback; each completed iteration adds exactly one evaluation. Stateful callbacks are accepted syntactically but deterministic semantics require equal values at equal arguments. Panics and callback allocations are not caught.


### tests

#### Executable checks

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

17 translated quadratics; absolute-value cusp; monotone endpoint; zero budget and exact callback counts; invalid interval callback not invoked; NaN callback; adjacent floats; repeated exponential fixture.

Independent oracle: The analytic quadratic optimizer c and abs(x-.137) cusp are independent of interpolation logic. Their tolerances constrain returned location and bracket; the monotone linear oracle constrains the endpoint limit.

Compiled negative control: Reverse fu<=fx to fu>=fx; quadratic_oracle must fail its status/location assertion after successful compilation.

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 fu<=fx to fu>=fx; quadratic_oracle must fail its status/location assertion after successful compilation.

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.