Optimization Problem with Error using optim.prob​lemdef.Opt​imizationP​roblem/sol​ve

Hi, I'm currrently working on creating an optimization problem that finds the maximum of an equation that has 3 constraints. My code is:

prob = optimproblem('ObjectiveSense','max');
x=optimvar('x',2,1);
prob.Objective = 1+(x(1))^2 * ((x(2)-1)^3) * (exp(-x(1)-x(2)));
cons1 = x(2) >= log(x(1));
cons2 = x(1) + x(2) <= 6;
prob.Constraints.cons1 = cons1;
prob.Constraints.cons2 = cons2;
show(prob);
sol=solve(prob);
sol.x; 

I keep getting the same errors:

Error using optim.problemdef.OptimizationProblem/solve

SOLVE requires a non-empty initial point structure to solve a nonlinear problem.

Please let me know if you have any advice. Thanks!

Answer 1

[Matt J]

Since your problem only has two unknowns, you can do a surface plot of the objective to find a decent initial guess.

[Jason Qian]

Thanks so much for the answer. How would you go about creating a surface plot to find a good initial guess? How would I be able to add the constraints into the surface plot?

[X,Y] = meshgrid(0:0.01:6,0:0.01:6);
Z = 1+(x)^2 * ((y-1)^3) * (exp(-x-y));
surf(X,Y,Z)

[Matt J]

[X,Y] = meshgrid(0:0.005:6,0:0.005:6);
Z = 1+(X).^2 .* ((Y-1).^3) .* (exp(-X-Y));
Z(Y<log(X))=nan;
Z(X+Y>6)=nan;

[zmax,i]=max(Z(:));
sol0.x=[X(i),Y(i)], zmax %Initial guess

sol0 = struct with fields:
    x: [2 4]

zmax = 1.2677

h=surf(X,Y,Z,'EdgeColor','none','FaceAlpha',0.5);
xlabel 'X'; ylabel 'Y';

prob = optimproblem('ObjectiveSense','max');
x=optimvar('x',2,1,'LowerBound',0,'UpperBound',6);
prob.Objective = 1+(x(1))^2 * ((x(2)-1)^3) * (exp(-x(1)-x(2)));
cons1 = x(2) >= log(x(1));
cons2 = x(1) + x(2) <= 6;
prob.Constraints.cons1 = cons1;
prob.Constraints.cons2 = cons2;

[sol,zopt]=solve(prob,sol0);

Solving problem using fmincon.

Initial point is a local minimum that satisfies the constraints.

Optimization completed because at the initial point, the objective function is non-decreasing 
in feasible directions to within the value of the optimality tolerance, and 
constraints are satisfied to within the value of the constraint tolerance.

sol.x, zopt

ans = 2×1

2 4

zopt = 1.2677

[Jason Qian]

Thank you so much. That makes a lot more sense. I really appreciate all the help!

[Matt J]

You're quite welcome, but please Accept-click the answer to indicate that it resolved your question.