Taking part in the boundary calculation from the function

Dear All,

I have a question regarding optimization calculations. I would like one of the boundary variables (M) to be calculated from the main function. Specifically, I have a program where I want to determine the value of M using the main function , and I would like to set this value as the upper boundary. Additionally, this value of M will change in each iteration based on the suggested value of x.

function [EFFT]=optimizpandy(x)
A1=x(1);
A2=x(2);
A3=x(3);
M=A1+A2;
EFFT=A1+A2^2+A3;
end
x0=[0.0019998     0.023       0.0019998 ];
lb=[0.001         0.02         0.001    ];
ub=[0.004         0.08         (M)-0.0001  ];
x= fmincon(@optimizpandy,x0,[],[],[],[],lb,ub);

Answer 1

[Steven Lord]

So you want to ensure that x(3) <= x(1)+x(2)-0.0001? That's not a bound, that's a linear constraint.

Write it as -x(1)-x(2)+x(3) <= -0.0001 and specify it using the A and b inputs to fmincon.

[mohammed hussein]

Thank you for your reply and suggestion . I want M to be calculated during the optimization process. My program is more complex than this example. Although this example may seem easy, I use it only to explain my problem.

[Torsten]

lb and ub for x(3) must be constants and mustn't depend on solution variables. As correctly noted by @Steven Lord, you have to formulate this restriction as a linear constraint:

x0 = [0.0019998     0.023       0.0019998 ];
lb = [0.001         0.02         0.001    ];
ub = [0.004         0.08         Inf  ];
A = [-1 -1 1];
b = -0.0001;
x = fmincon(@optimizpandy,x0,A,b,[],[],lb,ub)

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.

x = 1×3

0.0010 0.0200 0.0010

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function [EFFT]=optimizpandy(x)
  A1=x(1);
  A2=x(2);
  A3=x(3);
  EFFT=A1+A2^2+A3;
end

[Matt J]

I want M to be calculated during the optimization process. My program is more complex than this example.

If you mean that M(x) is, more generally, a nonlinear function of x, then the constraints are nonlinear, and you must express them using the nonlcon argument,

[mohammed hussein]

I will try to use this note. Thank you!