% Unconstrained optimization in the AnyBody Modeling System
% using a golden section method and steeoest descen search
% directions. Notice that this may not work if the problem
% is non-smooth.
% The side constraints, xmin and xmax, are handled by means of
% an exterior penalty function.

nOptimParam = 6;  % Number of design variables

% Design variables as they appear in the AnyScript model
    % AnyVar L0 = 0.24;             //Spring slack length
    % AnyVar F1 = 100;              //Spring force at 50% strain
    % AnyVar SpringRad = 0.15;      //Radius of spring attachment on the crank
    % AnyVar SpringAngle = 45;      //Angle of spring attachment points on the crank
    % AnyVar SpringX = -0.10;       //X coordinate of spring attachment on frame
    % AnyVar SpringY = 0.30
    
% Initialize 
%        L0        F1    SpringRad  SpringAngle   SpringY
xmin = [0.1       0.0      0.01        0.0         0.1];   % Lower bound
x =    [0.20    150.0      0.11       56.0         0.3];   % Initial guess
xmax = [0.4    1000.0      0.40      180.0         0.5];   % Upper bound

% Compute initial objective function value
F = ObjectivePenal(xmin,x,xmax);

% do optimization
maxiter = 10;
evals = 0;
delta = 0.1;  % Relative perturbation

while evals<maxiter
    % Compute gradient
    for j=1:length(x)
        xp = x;
        pert = (xmax(j)-xmin(j))*delta;
        xp(j) = xp(j)+pert;
        Fp = ObjectivePenal(xmin,xp,xmax);
        d(j) = -(Fp-F)/pert;
    end
    [x F] = goldengrad(xmin,x,xmax,d,10);    % Perform golden section optimization in that direction
    evals = evals + 1;
end