Using fmincon with a for loop

I am working on an optimization problem the first time for about 8 years. I am struggling with my for-loop.

The story behind the problem. I want to know, how high is the optimal investment for each period. I looked at you tube and found this video: "Application of Nonlinear Programming in Matlab"

The set up of my problem follows that in the video. First fmincon:

%%Setup for fmincon

LB = [0]; %vector with lower bounds
UB = inf; %vector with upper bounds

A = []; % No linear inequality constraints
B = [];
Aeq = []; %No linear equality contraints
Beq = [];

i0=0.1; %initial guess (starting point for iterations)

options = optimoptions('fmincon','Algorithm','sqp', 'Display','iter-detailed',...
'MaxFunctionEvaluations',100000,'MaxIterations',2000,'FunctionTolerance', 1e-10);

[i, present_value]=fmincon(@(i) obj_function_Diss(i), i0, A, B, Aeq, Beq, LB, UB, @(i) nonlcon_Diss(i), options)

Second the nonlcon:

function [cc, ceq] = nonlcon_Diss(i)
a=1; %lifetime of oldest machine
b=2; 
k=0.8; 
t=a+1;
z = 1;
y=b*i(z);
c = i(z)+k*(t-z)*b*i(z)/y;

ceq(1)=i(z)-c+k*(t-z)*b*i(z)/y;
ceq(2)=b*i(z)-y;

cc=[];

Third the objective function:

function present_value = obj_function_Diss(i)

a=1; %Age of oldest machine
b=2; %investment factor, should be bigger than 1
k=0.8; %cost factor
r=0.1; %interest rate
cum_present_value=0; %variable to cummulate the present value
t=a+1; %date of calculation
present_value = (b*i(z)-(i(z)+k*(t-z)*b*i(z)/b*i(z)))*exp(t*r*(-1));
cum_present_value=cum_present_value+present_value;
end
present_value=cum_present_value;
When you look at the code you can see, that I have set a=1. In this case it works. When I want to increase a e.g. to 4 or 7 or any other number, it is not working. I get the alert: "Index exceeds matrix dimensions."

Increasing "a" convert that single-period problem to a multi period problem. What do I have to change? And another question, imagine, I like to optimize i and a at the same time. How do I have to change the code?

If you need more information or have any other remarks please don't hesitate to answer. Thank you

Answer 1

[Ameer Hamza]

You can use fmincon to solve a multivariate optimization problem. You need to make following changes in the code.

• Change LB and UB for 2 variable case

LB = [0; 0]; %vector with lower bounds
UB = [inf, inf]; %vector with upper bounds

• Define initial condition for both variables and combine them in one array. Here, I named combined array as x. Remember the first and second element of x correspond to values of a and i respectively.

i0=0.2; %initial guess (starting point for iterations)
a0=0.5;
x0=[a0 i0];

• Also change the nonlinear constraint function because the input is 2 element vector.

function [cc, ceq] = nonlcon_Diss(x)
  a=x(1); %lifetime of oldest machine
  i=x(2);

• Similarly change objective function

function present_value = obj_function_Diss(x)
  a=x(1); %Age of oldest machine
  i=x(2);

You can follow the same procedure to optimize several variables. The complete modified is also attached.