Module optimization 

Optimization: continuous, combinatorial, and strategic.

The module root holds the scalar and unconstrained-gradient methods – golden section and Brent for a bracketed minimum of one variable, then gradient descent with and without momentum, Adam, numerical gradients, and the regression and curve fitting built on them.

The submodules take it further: lp for linear programming and duality, integer for branch-and-bound and dynamic programming, network for flows and scheduling, convex for L-BFGS, proximal methods and ADMM, metaheuristics for the derivative-free and population-based methods, game_theory for equilibria and cooperative solutions, and least_squares for Levenberg-Marquardt.

Re-exports

pub use least_squares::fit_exponential_decay;

pub use least_squares::fit_gaussian_peak;

pub use least_squares::levenberg_marquardt;

pub use least_squares::LmResult;

Modules

convex

Convex optimisation: gradient methods, quasi-Newton methods, proximal splitting, and constrained solvers.

game_theory

Game theory: equilibria, dynamics, cooperative solution concepts, auctions, and two-player search.

integer

Integer programming, dynamic programming, and combinatorial search.

least_squares

Nonlinear least squares: Levenberg-Marquardt.

lp

Linear programming: the simplex method, interior point methods, duality, and the classical models that reduce to a linear program.

metaheuristics

Derivative-free and population-based optimisation, and the benchmark landscapes used to tell one method from another.

network

Network models and scheduling: project planning, flows on networks, and the sequencing rules that provably optimise a stated objective.

Functions

adam

Adam optimizer (β1=0.9, β2=0.999, ε=1e-8).

brent_min

Brent’s method for 1-D minimization, combining golden-section search with parabolic interpolation.

golden_section_min

Golden-section search for the minimum of f on [a, b].

gradient_descent

Vanilla gradient descent: x ← x − α∇f.

gradient_descent_momentum

Gradient descent with momentum: v ← μv − α∇f, x ← x + v.

linear_regression

Ordinary linear regression: minimizes ‖a0 + a1·x − y‖₂ via Householder-QR least squares (linalg::qr::least_squares).

nelder_mead

Nelder-Mead simplex algorithm for unconstrained minimization.

numerical_gradient_vec

Central-difference numerical gradient of a scalar function of n variables.

polynomial_fit

Fit a polynomial of the given degree to (x, y) data by QR least squares on the Vandermonde matrix, falling back to normal equations with Gaussian elimination when the system is rank deficient.

r_squared

Coefficient of determination R² = 1 − SS_res / SS_tot.

simulated_annealing

Simulated annealing for unconstrained minimization.