📐algorithm-projected-gradient-box-tests

The groupant beside algorithms/src/projected_gradient_box/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

Components

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.

Model text

descriptant

projected_gradient_box finite checks

The test harness observes finite assertions on projected_gradient_box. 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

13 diagonal cases compared to clipped analytic minimizers; dense 2x2 stationary optimizer [1,2] and objective -7.5; linear objective with zero Q; zero budget; negative diagonal, asymmetric and empty matrix rejection.

Limits

Projected-step residual<=tolerance precedes budget exhaustion. Each update swaps buffers, preserving coordinate order. The equality stagnation guard is presently dominated by the residual-zero convergence test for finite values and positive tolerance; Status::Stagnated is shared but this branch is unreachable in this scoped arithmetic model. No unsupported stagnation coverage is claimed. No timing or universal machine-accuracy claim.

Reference: Bertsekas, Nonlinear Programming (1999); Nocedal and Wright, Numerical Optimization (2006).

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 f(x)=.5x'Qx-b'x on lower<=x<=upper. Validate exact symmetry and nonnegative diagonal; off-diagonal row absolute sum must be zero or below diagonal/(1+128*EPSILON), a conservative sufficient PSD domain. L=max(max row absolute sum,1e-100). Clip initial point, then x_next=clip(x-(Qx-b)/L). Residual=max_i|x_i-x_next_i| is a projected-step observation, not gradient norm or solution distance.

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: 13 diagonal cases compared to clipped analytic minimizers; dense 2x2 stationary optimizer [1,2] and objective -7.5; linear objective with zero Q; zero budget; negative diagonal, asymmetric and empty matrix rejection.

Composition limits: Dimension/value/matrix validation precedes bound validation, both precede checked allocation of x, gradient, next. Failed try_reserve maps to AllocationFailed. Iteration order ascending, no callbacks. Caller matrix memory O(n²) excluded from scratch cost. Zero Q uses tiny positive scale and often jumps to an active box endpoint. Projected-step residual<=tolerance precedes budget exhaustion. Each update swaps buffers, preserving coordinate order. The equality stagnation guard is presently dominated by the residual-zero convergence test for finite values and positive tolerance; Status::Stagnated is shared but this branch is unreachable in this scoped arithmetic model. No unsupported stagnation coverage is claimed.

approximant

Forward approximant and invariant

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

Domain and invariant

n in 1..64, finite operands abs<=1e50, exact rectangular shape and symmetry, finite positive tolerance, budget<=100000; then finite ordered bounds. Nonfinite objective, gradient or raw step is NonFiniteArithmetic. Summed diagonal dominance includes a safety margin but is not a general floating PSD certification.

Diagonal Q has exact optimizer clip(b_i/Q_ii); dense example directly satisfies Q*[1,2]=[5,5]. These independent identities verify location and objective without replaying projected iterations.

Cost

O(n²) validation and O(k*n²) arithmetic; O(n) additional storage (three length-n vectors), 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: Bertsekas, Nonlinear Programming (1999); Nocedal and Wright, Numerical Optimization (2006).

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: 13 diagonal cases compared to clipped analytic minimizers; dense 2x2 stationary optimizer [1,2] and objective -7.5; linear objective with zero Q; zero budget; negative diagonal, asymmetric and empty matrix 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 Diagonal Q has exact optimizer clip(b_i/Q_ii); dense example directly satisfies Q*[1,2]=[5,5]. These independent identities verify location and objective without replaying projected iterations.. Many different update orders or untested behaviors have the same pass transcript, so source recovery is not unique.

independent_oracle

Diagonal Q has exact optimizer clip(b_i/Q_ii); dense example directly satisfies Q*[1,2]=[5,5]. These independent identities verify location and objective without replaying projected iterations.

mutation_sensitivity

Change shared gradient dot-b to dot+b; diagonal_clipping_oracle must reject the compiled incorrect optimization direction.

boundary_partition

A zero matrix is valid, while a negative diagonal or asymmetric matrix fails before allocation. Linear box optimum is an endpoint; a zero budget returns the clipped initial point and its observed projected residual.

tests

Executable checks

Run cargo test -p mova-algorithms projected_gradient_box::tests.

13 diagonal cases compared to clipped analytic minimizers; dense 2x2 stationary optimizer [1,2] and objective -7.5; linear objective with zero Q; zero budget; negative diagonal, asymmetric and empty matrix rejection.

Independent oracle: Diagonal Q has exact optimizer clip(b_i/Q_ii); dense example directly satisfies Q*[1,2]=[5,5]. These independent identities verify location and objective without replaying projected iterations.

Compiled negative control: Change shared gradient dot-b to dot+b; diagonal_clipping_oracle must reject the compiled incorrect optimization direction.

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+calphaslope, 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: Change shared gradient dot-b to dot+b; diagonal_clipping_oracle must reject the compiled incorrect optimization direction.

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.

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