MATLAB: How to use fmincon solver for optimising a continuously varying function

non linear optimisationoptimisation toolsolvers

I need to optimize a function of the form

y(i)= exp(-a(i)/x(1)) + 1.285 + ((b(i)^2)*x(2)) - (x(3)*c(i)*(1-exp(-c(i)/(x(3)*x(2))));

a(i) and c(i) are inputs. b(i) is dependant on a(i). The matrices a,b,c are obtained first. x(1),x(2),x(3) are the coefficients to be optimized. x>=0 .

When I try to use fmincon solver, it returns an error ::

Error using fmincon (line 607)
User supplied objective function must return a scalar value.

How do I rectify this?

Thanks

Nadia

Best Answer

function y = obj(x, a, b, c)
  y = sum( ( exp(-a./x(1)) + 1.285 + ((b.^2).*x(2)) - (x(3).*c.*(1-exp(-c./(x(3).*x(2))))) ).^2 );

You need to recheck your equation as you have a missing ")" in it. I put it at the end.

To use the above:

fmincon( @(x) obj(x, a, b, c), x0, .....)

What will be minimized is the sum of squares. This is, in other words, a least squared minimimization.

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MATLAB: Problems with fmincon, how to solve

Your problem is convex, so you can use the CVX package if you want. Also, the solution should be the global minimum; not a local minimum. To use fmincon, do the following:

Equality/nonEquality constraint:

function [c,ceq]=mycon(x)
c(1) = x(1)^2 + x(2)^2 - 4*x(1) - 3*x(2) + 5;
c(2) = -x(1)^2 - x(2)^2 + 4*x(1) + 3*x(2) - 6; % notice the fixed typo
ceq = 2*x(1)^2 + 2*x(2)^2 - 3*x(1) - 3*x(2) - 2; 
end

Construct the problem and call fmincon:

clc
clear all
Aeq=[]; 
beq=[]; 
A=[]; 
b=[]; 
% if you are not sure that vector x is within lb and ub do not restrict it
lb = []; %lb=[-3,-3]; 
ub = []; %ub=[3,3]; % 
x0=[4,4];
myObj = @(x) x(1)^2 + x(2)^2 - 5*x(1) - 6*x(2) + 15;
nonlcon = @mycon;
options = optimoptions('fmincon','Algorithm','sqp','Display','iter-detailed','MaxFunctionEvaluations',100000, 'MaxIterations',2000, 'OptimalityTolerance' ,1e-10);
[x,cost] = fmincon(myObj,x0,A,b,Aeq,beq,lb,ub,nonlcon)

Output (global minimum):


Local minimum found that satisfies the constraints.
Optimization completed because 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.
<stopping criteria details>
x =
    1.6450    1.9007
cost =
    1.6896

MATLAB: Displaying lsqnonlin estimation values at each iteration

See the OutputFcn example. The example does basically exactly what you ask. It is written for fmincon, but applies to lsqnonlin as well.

Best Answer

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MATLAB: Problems with fmincon, how to solve

MATLAB: Displaying lsqnonlin estimation values at each iteration

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