/**
 * Result of `nelderMead` and `gradientDescent`: the best point `x`,
 * its value `fx`, the iteration count, and a convergence flag.
 */
export interface OptimizeResult {
    x: number[];
    fx: number;
    iterations: number;
    converged: boolean;
}
/**
 * Nelder–Mead downhill-simplex minimization of `f: ℝⁿ → ℝ` from `x0`. Derivative-free.
 * Matches `scipy.optimize.minimize(method='Nelder-Mead')` to the requested tolerance.
 */
export declare function nelderMead(f: (x: number[]) => number, x0: readonly number[], opts?: {
    maxIter?: number;
    tol?: number;
    step?: number;
}): OptimizeResult;
/**
 * Gradient-descent minimization with optional backtracking line search. `grad` may
 * be supplied; otherwise a central-difference gradient is used.
 */
export declare function gradientDescent(f: (x: number[]) => number, x0: readonly number[], opts?: {
    grad?: (x: number[]) => number[];
    rate?: number;
    maxIter?: number;
    tol?: number;
}): OptimizeResult;
/**
 * Result of `levenbergMarquardt`: the solution `x`, the residual norm, the iteration
 * count, and a convergence flag.
 */
export interface LMResult {
    x: number[];
    residualNorm: number;
    iterations: number;
    converged: boolean;
}
/**
 * Levenberg–Marquardt nonlinear least squares: minimize ½‖r(x)‖² for a vector
 * residual `r`. Numeric Jacobian; damped normal equations `(JᵀJ + λI)δ = Jᵀr`
 * solved via the matrix `inv`. Mirrors `scipy.optimize.least_squares(method='lm')`.
 */
export declare function levenbergMarquardt(residual: (x: number[]) => number[], x0: readonly number[], opts?: {
    maxIter?: number;
    tol?: number;
}): LMResult;
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