The return value of the objective callback function must be a real double scalar.

Dear friends,

I am trying to do a Mixed Integer Nonlinear Program (MINLP) Optimization problem by using a "BONMIN" toolbox. I have got an error and couldn't find the problem.

This is my code:

clc,clear
a = 1000; 
b = 0.05;
h = 1;
c = 8;
i = 0.02;
r = 0.08;
T_0 = 0.06;
m = 0.5;
O = 200;

syms v x t T p k

%theta
theta = 1/(1+m-v);

inner1 = int(theta, 0, x);
outer1 = int(exp(inner1), 0, T);
inner2 = int(theta, t, x);
outer2 = int(int(exp(inner2), t, T), 0, T);

Warning: Unable to check whether the integrand exists everywhere on the integration interval.

outer3 = int(outer1,0,T)

Warning: Unable to check whether the integrand exists everywhere on the integration interval.

outer3 = 

%Objective function
TP = (a*exp(-b*p)/T)*((p-c*(1+i*k)*(1+r*(T-(k+1)*T_0/2)))*outer1-(h+r*h*p)*outer2+r*p*outer3)-O/T

TP = 

f = -TP 

f = 

x = sym('x', [3, 1])  

x = 

tn= ['fun_1','.m'];
fun_1 = matlabFunction(subs(f, [k, p, T], [x(1),x(2),x(3)]),'file',tn)

fun_1 = function_handle with value:
    @fun_1

fun = @(x) fun_1(x(1),x(2),x(3))

fun = function_handle with value:
    @(x)fun_1(x(1),x(2),x(3))

nlcon = @(x)  x(3)-T_0*x(1);
cl = 0;
cu = Inf;  
lb = [1;c;T_0];
ub = [floor(m/T_0);Inf;m];  
x0 = [2 12 0.2]';  
opts = optimset('display','iter');
xtype = 'ICC';
Opt = opti('fun',fun,'nl',nlcon,cl,cu,'bounds',lb,ub,'xtype',xtype,'x0',x0,'options',opts)%½¨Á¢¶ÔÏó:×¢Òâ°Ñº¯Êý¡¢Ô¼ÊøÌõ¼þ¡¢±ß½ç¡¢±äÁ¿ÀàÐÍ¡¢³õÖµµÈ¶¼°üº¬½øÀ´

Unrecognized function or variable 'opti'.

[x,fval,exitflag,info] = solve(Opt)% Çó½â

The following is the error obtained :

*** Error using Bonmin Matlab interface: ***

The first return value of the objective callback function must be a real double scalar.

Exception of type: IpoptException in file "Unknown File" at line -1:

Exception message: Unknown Exception caught in Ipopt

NLP0012I

Num Status Obj It time Location

NLP0014I 1 FAILED 0 0 0

*** Error using Bonmin Matlab interface: ***

The first return value of the objective callback function must be a real double scalar.

Exception of type: IpoptException in file "Unknown File" at line -1:

Exception message: Unknown Exception caught in Ipopt

NLP0014I 1 FAILED 0 0 0 resolve robustness

*** Error using Bonmin Matlab interface: ***

The first return value of the objective callback function must be a real double scalar.

Exception of type: IpoptException in file "Unknown File" at line -1:

Exception message: Unknown Exception caught in Ipopt

NLP0014I 3 FAILED 0 0 0

Cbc0006I The LP relaxation is infeasible or too expensive

Answer 1

[Torsten]

Looking at your objective function, it seems it it returns complex values. This will make MATLAB error - you cannot minimize a function that is complex-valued.

[国静]

Thanks for your reply, I have carefully checked my objective function and redefined it, which has solved the problem. Thanks again!