How should I use Fmincon function when I just have linear constraints but Nonlinear objective function?

Hi my objective function is nonlinear, and my only constraints are:

x(1)<0.00125
x(1)>0
x(2)>0

And I wanna solve it with interior point optimzation method I get error for this code :

x0=[1.1;3];    % Starting guess 
B = [1.25;20.0];      
A = [1,0;0,1];  
lb=[0.5;0.4];    
up=[1.25;20.0];
Aeq=[];
beq=[];
options=optimset('outputfcn',@outfun,'Largescale','off','Algorithm','interior-point','Display','iter','Tolx',1e-15,'Tolfun',1e-16,'MaxFunEvals',60000,'MaxIter',1000); 
[x,fval,exitflag,output]=fmincon(@optim,x0,A,B,Aeq,beq,lb,ub,options);

it said I need a nonlcons in my Fmincon function So I add this function

function [c,ceq]=const(x)
c(1)=x(1)-0.00125;
c(2)=-x(1);
c(3)=-x(2);
ceq=[];
end
and add these to my code:

nonlcon=@const
[x,fval,exitflag,output]=fmincon(@optim,x0,A,B,Aeq,beq,lb,ub,'nonlcon',options);

But I still get error for this nonlcon :(

Answer 1

[Alan Weiss]

Your problem is that you are using options in the place where fmincon expects to see nonlinear constraints. In other words, your call should be

[x,fval,exitflag,output]=fmincon(@optim,x0,A,B,Aeq,beq,lb,ub,[],options);

But wait, there's more. You should NOT use A and B to set bounds. And you have lb and ub that do not make sense to me, because you say that your only constraints are x(i) > 0 and x(1) < 0.00125. So get rid of A, B, nonlcon, and set

lb = [0,0];
ub = [0.00125,Inf];
[x,fval,exitflag,output]=fmincon(@optim,x0,[],[],[],[],lb,ub,[],options);

Alan Weiss

MATLAB mathematical toolbox documentation

[NooshinY]

Thank you so much let me try it

[NooshinY]

I still get this error:

Error in finDiffEvalAndChkErr

Error in finitedifferences

Error in computeFinDiffGradAndJac

Error in barrier

Error in fmincon (line 800)
    [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...

Error in final (line 12)
[x,fval,exitflag,output]=fmincon(@optim,x0,[],[],[],[],lb,ub,[],options);

[Alan Weiss]

Please give the full error message, copy-pasted from your MATLAB session.

Also, please give the results of executing

f = optim(x0)
f1 = optim(x0 + randn(size(x0)))

Alan Weiss

MATLAB mathematical toolbox documentation

[NooshinY]

I got this error for f=optim(X0) f1=optim(x0+rand(size(x0)))

Subscript indices must either be real positive integers or logicals.

Error in MyF (line 15)
R(t,m)=((0.5*(1+erf((D-miuw)/(sqrt(2)*sw)))).^m )*(poisspdf(m,lamda.*t))*numconv(H,m,t);

Error in optim (line 12)
     Inspcost1(j)=MyF(x(1),t1(j));

Error in final (line 13)
f1 = optim(x0 + randn(size(x0)))

[NooshinY]

and this is my MyF function:

function A=MyF(H,t)
%H=0.00125;
D=1.5;
lamda=2.5*10^(-2);
miuw=1.2;
sw=0.2;
dis=zeros(10,10);
%for t=1:20
for m=1:5 %number of shocks
part1=((0.5*(1+erf((D-miuw)/(sqrt(2)*sw)))).^m );
%part2(m)=(exp(-lamda.*t).*((lamda.*t).^(m))./factorial(m))
part2=poisspdf(m,lamda.*t);
%part12(m)=((0.5*(1+erf((D-miuw)/(sqrt(2)*sw)))).^m ).*(exp(-lamda.*t).*((lamda.*t).^(m))./factorial(m))
part3=numconv(H,m,t);
R(t,m)=((0.5*(1+erf((D-miuw)/(sqrt(2)*sw)))).^m )*(poisspdf(m,lamda.*t))*numconv(H,m,t);
end
format long
F(t)=1-sum(R(t,:));
%end
A=F(t)

[NooshinY]

and this is the numconv function:

function U=numconv(H,m,t)
alpha=0.1;
beta=0.1;
alpha2=0.2;
syms G g1 u x;
Q=@(u)(gamcdf(H-u,alpha.*t,beta)).*(beta.^(m.*alpha2).*(u.^((m.*alpha2)-1)).*exp(-beta.*u))./gamma(m.*alpha2);
Q1=quad(Q,0,H);
U=quad(Q,0,H)

[Alan Weiss]

I understand the result of this experiment is that your objective function throws an error for some points, I suspect for points that are not integer-valued. I suggest that you use the debugger to find out why your objective function throws an error for some points. fmincon works for continuous problems, meaning the objective function must be able to be evaluated for real points that are not restricted to integer values.

Alan Weiss

MATLAB mathematical toolbox documentation