Function constrainedGaussNewton

constrainedGaussNewton(
    initialParameters: Float64Array,
    initialStates: Float64Array,
    residualFunction: ConstrainedResidualFn,
    constraintFunction: ConstraintFn,
    options?: ConstrainedGaussNewtonOptions,
): ConstrainedGaussNewtonResult
Performs constrained Gauss-Newton optimization for nonlinear least squares problems.

Algorithm:
1. Start with initial parameters p0 and states x0 (satisfying c(p0, x0) = 0)
2. Compute effective Jacobian J_eff = r_p - r_x C_x^+ C_p
3. Solve normal equations: (J_eff^T J_eff) δ = -J_eff^T r
4. Update parameters: p_new = p_old + δ
5. Update states: x_new = x_old + dx where (∂c/∂x) dx = -∂c/∂p · δ (linear approximation)
6. Repeat until convergence
The effective Jacobian captures all constraint effects, allowing the algorithm to use the same structure as unconstrained Gauss-Newton.
Parameters
- initialParameters: Float64Array
  Initial parameter vector p0
- initialStates: Float64Array
  Initial state vector x0 (should satisfy c(p0, x0) = 0)
- residualFunction: ConstrainedResidualFn
  Residual function r(p, x)
- constraintFunction: ConstraintFn
  Constraint function c(p, x) = 0
- options: ConstrainedGaussNewtonOptions = {}
  Optimization options
Returns ConstrainedGaussNewtonResult
Optimization result with final parameters, states, and constraint norm
- Defined in core/constrainedGaussNewton.ts:480