What code are you running in the command window vs the live script? I get the same result running the following code in both places:
clear all
sympref('AbbreviateOutput',false); sympref('MatrixWithSquareBrackets',true);
syms x1 x2
f = -x1*x2 %objective function
g1 = (1/9)*x1^2 + (1/4)*x2^2 - 1 %given inequality constraint
g2 = -x1 %bounds set as inequality constraints
g3 = x1 - 3
g4 = -x2
g5 = x2 - 2
lambda_j = 1 %initialize inequality lagrange parameter
rp = 1 %initialize penalty parameter
b = 20 %initialize penalty adjustment parameter 'beta'
k = 1; %first ALM iteration
x = [2.5; 1.6] %initial design point
psi_j = max(subs(g1,[x1;x2],x), -lambda_j/(2*rp))
if subs(g1,[x1;x2],x) > 0 %if inequality is violated
A = f + lambda_j*psi_j + rp*psi_j^2
else %if no constraints are violated
A = f
end
c = subs(gradient(A),[x1;x2],x) %gradient of objective function at current point
d = -c
% Analytically solve for astar
syms alpha_star
xnew = x + alpha_star*d %update design point with alpha_star
% Solve for alpha using necessary condition df/da = 0
fa = subs(A,[x1;x2],xnew) %create alpha function
df_da = diff(fa)
astar = solve(df_da,alpha_star);
displaySymSolution(astar);
s = astar*d %calclulate the change in design
xnew = x + astar*d %update design point numerically
x = xnew;
lambda_j + 2*rp*max(subs(g1,[x1;x2],x), -lambda_j/(2*rp))
