How to avoid a negative solution with fmincon, including an external equation?
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Hello community,
I want to create an optimization script with fmincon, including an equation (f2), which is not solved by fmincon. This equation will be solved with a function (see bottom of the script in the function 'kostfunktion'), but it contains the parameters x(1) and x(2) from the optimization problem. The problem is, that f2 and therefore fval are always negative. How can I set these parameters to a minimum of 0 or at least let them be positive?
The involving case is this one:
- f1 = 10*x1 + 2*x2 - 30 f2 = - 2*x1 - 10*x2 + 30
Bounds: 1<=x1<=5 1<=x2<=5 0<=f1<=inf 0<=f2<=inf
The optimization goal is to get the minimum of: obj = f1 + f2
f1 will be solved by fmincon. f2 will be solved in the function 'kostfunktion'.
clc, clear, clear global;
global f2 %f2 appears in the workspace, just to be visible
x0 = [2; 2; 1]; % [x1, x2, f1]
A = [];
b = [];
Aeq = [-10 -2 1];
beq = [-30];
lb = [1; 1; 0];
ub = [5; 5; inf];
options = optimoptions('fmincon', 'Display', 'iter');
[x fval] = fmincon(@kostfunktion,x0,A,b,Aeq,beq,lb,ub,[],options);
function obj = kostfunktion(x)
global f2
f2 = -2*x(1)-10*x(2)+30;
obj = x(3) + f2; % obj = f1 (solved with fmincon) + f2 (solved with this function)
end
The optimal solution should be obj = 0 with x1 = 2.5 and x2 = 2.5, but in this script, the solution is obj = -24, because I can't set bounds for f2. How can I set the bounds for f2 or fval?
Thanks for your support.
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채택된 답변
Bruno Luong
2021년 4월 28일
편집: Bruno Luong
2021년 4월 28일
The condition
f2 = - 2*x1 - 10*x2 + 30 >= 0
is equivalen to
2*x1 + 10*x2 + 0*f1 <= 30.
So set
A = [2 10 0]
b = 30
If you don't want to use A/b arguments (since f2 can be changed to more generic non linear function), just use non linear constraint nonlcon argument and program c output that handles that constraint.
댓글 수: 6
Bruno Luong
2021년 4월 28일
Use A/b
x0 = [2; 2; 1]; % [x1, x2, f1]
A = [2 10 0]
b = 30;
Aeq = [-10 -2 1];
beq = [-30];
lb = [1; 1; 0];
ub = [5; 5; inf];
options = optimoptions('fmincon', 'Display', 'iter');
[x fval] = fmincon(@kostfunktion,x0,A,b,Aeq,beq,lb,ub,[],options);
x
function obj = kostfunktion(x)
global f2
f2 = -2*x(1)-10*x(2)+30;
obj = x(3) + f2; % obj = f1 (solved with fmincon) + f2 (solved with this function)
end
추가 답변 (2개)
Matt J
2021년 4월 28일
편집: Matt J
2021년 4월 28일
Since your problem is linear, let's just use linprog,
%Reformulate with x=[x1,x2,f1,f2]
A = [];
b = [];
Aeq = [-10 -2 1 0;
2 10 0 1 ];
beq = [-30;+30];
lb = [1; 1; 0; 0];
ub = [5; 5; inf; inf];
obj=[0 0 1 1];
x=linprog(obj,A,b,Aeq,beq,lb,ub)
댓글 수: 9
Matt J
2021년 4월 28일
I don't understand what the "MathWorks Service" refers to here. You said you have many optimization problems to solve and you are looping over them, each time calling fmincon to get a solution. Why can't you feed a different A,b,Aeq,beq to fmincon each time you call it?
Matt J
2021년 4월 28일
편집: Matt J
2021년 4월 28일
You could consider something like this:
x0 = [2; 2; 1]; % [x1, x2, f1]
A = [];
b = [];
Aeq = [-10 -2 1];
beq = [-30];
lb = [1; 1; 0];
ub = [5; 5; inf];
options = optimoptions('fmincon', 'Display', 'iter','Algorithm', 'sqp','MaxFunctionEvaluations',inf,...
'OptimalityTolerance',1e-12,'FunctionTolerance',1e-12,'StepTolerance',1e-12);
[x fval] = fmincon(@kostfunktion,x0,A,b,Aeq,beq,lb,ub,[],options)
function obj = kostfunktion(x)
global f2
f2 =-2*x(1)-10*x(2)+30;
c=10;
if f2<0, f2=exp(-c*f2)+c*f2-1; end %apply a penalty
obj = x(3) + f2; % obj = f1 (solved with fmincon) + f2 (solved with this function)
end
댓글 수: 8
Matt J
2021년 4월 28일
편집: Matt J
2021년 4월 28일
Yes, but why would you be attempting to make beq(2) evolve throughout the optimization?
If you have a constraint of the general form Aeq*x=h(x) where h(x) is a non-constant, non-linear function of x, then this is a non-linear constraint, and should be handled using the nonlcon input.
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