ArgMin

Optimization solver written by pure Julia

Solve constrained nonlinear least square with augmentedl lagrangian method

xhat = argmin(|f(x)|^2) s.t g(x) = 0

solve constrained least_square
xhat = argmin(|Ax = b|^2) s.t. Cx = d

solve least square
xhat = argmin(|Ax = b|^2)

All are same solution 
- xhat = inv(A’*A)*(A’*b)
- xhat = pinv(A)*b
- Q,R = qr(A); xhat = inv(R)*(Q’*b)
- xhat = A

solve multi objective least square
xhat = argmin(λ_1|Ax = b|^2+λ_2|Ax = b|^2...)

solve nonlinear least square with gauss-newton method

xhat = argmin(|f(x)|^2)

solve nonlinear least square with levenberg marquardt

xhat = argmin(|f(x)|^2)

solve nonlinear least square with newton-raphson method

The inputs have to be length(x) == length(f(x)).
If it is not, you cant use solve_nonlinear_least_square_with_gauss_newton

xhat = argmin(|f(x)|^2)

Solve quadratic programming with projected newton method

argmin(0.5*x'*H*x + x'*g)
s.t. lower<=x<=upper

inputs:
    H - positive definite matrix   (n * n)
    g - a vector                   (n)
    lower - lower bounds           (n)
    upper - upper bounds           (n)

optional inputs:
    x0       - initial state       (n)
    maxIter        = 100       maximum number of iterations
    minGrad        = 1e-8      minimum norm of non-fixed gradient
    minRelImprove  = 1e-8      minimum relative improvement
    stepDec        = 0.6      factor for decreasing stepsize
    minStep        = 1e-22    minimal stepsize for linesearch
    Armijo         = 0.1      Armijo parameter
    verbose        = false    verbosity

outputs:
    xstar    - solution            (n)
    status   - status dictionary