Module problem 

Problem traits the user implements about their objective. Solvers bind on whichever subset they need (e.g. gradient descent requires CostFunction and Gradient; Nelder-Mead only needs CostFunction).

Soft reject vs hard abort

Every problem trait method returns Result<_, Self::Error>. The two ways to signal “something went wrong” are deliberately distinct:

• Soft reject (Ok(f64::INFINITY)): return +∞ from CostFunction::cost to reject a single point. Line searches treat it as worse and retreat; population solvers treat it as worst fitness. This is the right channel for “this x is outside my domain, but the solve should continue.”
• Hard abort (Err(_)): return Err to terminate the entire solve. The error bubbles all the way out of Executor::run typed as Result<_, P::Error>. Use this when the failure is not about a particular x: a downstream service vanished, the user pressed cancel, an early-stopping criterion in the problem’s own state fired.

Problems that never fail in this way pick type Error = std::convert::Infallible; (or ! on nightly). Niche optimization collapses Result<f64, Infallible> to f64 layout, so the happy path stays zero-cost.

Structs

EvalCounts

Per-kind evaluation counters carried by Problem.

Problem

Counting wrapper that solvers receive instead of &P directly.

Traits

CostFunction

Scalar-valued objective f(x): Param → Output. The smallest problem trait: every solver binds at least on this.

Gradient

Analytic gradient ∇f(x): Param → Gradient. Required by first-order solvers (gradient descent, BFGS, …).

Hessian

Analytic Hessian H(x) = ∇²f(x): Param → Hessian for second-order solvers (Newton, trust-region-Newton). The associated Hessian matrix type lets solvers bound on the linear-algebra ops they need (LinearSolveSpd, SymmetricEigen, …) without baking in a backend.

HessianProduct

Matrix-free Hessian-vector products: v ↦ ∇²f(param) · v.

Jacobian

Analytic Jacobian J(x) = ∂r/∂x: Param → Jacobian for least-squares solvers (Gauss-Newton, LM, TRF). The associated Jacobian matrix type is what lets solvers bound on the linear-algebra ops they need (MatVec, LinearSolveSpd, …) without baking in a specific backend or assuming density.

MiniBatchGradient

Finite-sum gradient (1/|B|) Σ_{i ∈ B} ∇fᵢ(x) over a chosen subset B of component samples. Required by mini-batch stochastic solvers (Sgd), which call it once per step with a fresh batch of indices the solver drew from its own ChaCha8Rng.

Residual

Vector-valued residual r(x): Param → Output for least-squares problems. Required by Gauss-Newton, Levenberg-Marquardt, and any solver that minimizes ½‖r(x)‖².