When I use fmincon, the optimised result does not satisfy my non liner constraints
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clear variables
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clc
fun = @(x)4*x(1)+x(2);
x0=[0.4,0.28]
lb = [0.01,0.01];
ub = [5,0.8];
A = [];
b = [];
Aeq = [];
beq = [];
options = optimoptions('fmincon','Algorithm','sqp');
c = @(x)(4+4*x(1)+9*x(1)^2)*(1+x(1))^2-(2*x(1)^3*x(2)+2+3*x(1)+3*x(1)^2)^2+0.001;
nonlcon = @(x)deal(c(x),[]);
[x,fval,exitflag,output] = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options);
exitflag
checkinitialpoint=(4+4*x0(1)+9*x0(1)^2)*(1+x0(1))^2-(2*x0(1)^3*x0(2)+2+3*x0(1)+3*x0(1)^2)^2+0.001;
checkconstraits=(4+4*x(1)+9*x(1)^2)*(1+x(1))^2-(2*x(1)^3*x(2)+2+3*x(1)+3*x(1)^2)^2+0.001;
The above is my matlab code, I input the nonlear constraints, but the results give to me is obviously not satisfy the constraints (you can see that checkconstraits is positive), my initial point is within the range.
Can anyone help me? Many thanks.
1 Comment
Torsten
on 29 Aug 2023
The solver converged to an infeasible point (see above). Your observation is the same as the exitflag from "fmincon" indicates.
Answers (2)
Alan Weiss
on 29 Aug 2023
You would do better to use the default 'interior-point' algorithm, which arrives at a feasible solution.
fun = @(x)4*x(1)+x(2);
x0=[0.4,0.28];
lb = [0.01,0.01];
ub = [5,0.8];
A = [];
b = [];
Aeq = [];
beq = [];
% options = optimoptions('fmincon','Algorithm','sqp');
c = @(x)(4+4*x(1)+9*x(1)^2)*(1+x(1))^2-(2*x(1)^3*x(2)+2+3*x(1)+3*x(1)^2)^2+0.001;
nonlcon = @(x)deal(c(x),[]);
[x,fval,exitflag,output] = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon)
Alan Weiss
MATLAB mathematical toolbox documentation
Matt J
on 29 Aug 2023
Edited: Matt J
on 29 Aug 2023
Since it is a 2D problem, it practically begs you to pre-sweep for a good initial guess:
fun = @(x)4*x(1)+x(2);
lb = [0.01,0.01];
ub = [5,0.8];
A = [];
b = [];
Aeq = [];
beq = [];
c = @(x)(4+4*x(1)+9*x(1)^2)*(1+x(1))^2-(2*x(1)^3*x(2)+2+3*x(1)+3*x(1)^2)^2+0.001;
nonlcon = @(x)deal(c(x),[]);
[x0,fval0]=sweep(fun,c,lb,ub)
options = optimoptions('fmincon','Algorithm','sqp');
[x,fval,exitflag,output] = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options);
x,fval
function [x0,fval]=sweep(fun,c,lb,ub)
F=@(x1,x2) fun([x1,x2])+eps./(c([x1,x2])<=0);
[X1,X2]=ndgrid(linspace(lb(1),ub(1),30), linspace(lb(2),ub(2),30));
v=arrayfun(F,X1,X2);
[fval,i]=min(v(:));
if ~isfinite(fval)
disp 'No feasible point found'; x0=[];
else
x0=[X1(i),X2(i)];
end
end
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