MATLAB: How can we obtain the golobal minimum? in case nonconvex optimization using fmincon.

fmincon

in case our constraint functions are nonconvex how can we obtain the global minimun using fmincon?

Best Answer

If you need a global minima, then fmincon() is usually the wrong routine to use. fmincon() is a local minimizer. There are certain kinds of functions for which it will find the global minimum within the constraints, but not generally. If there is any location inside the constrained area where the partial derivatives are all nearly 0 then fmincon() may find that location even if the global minimum seems "obvious".

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MATLAB: How to find global minima using fmincon function and non-linear constraint

GlobalSearch and MultiStart use fmincon as the local solver, so they support whatever comstraints fmincon supports, meaning basically anything but integer or nonsmooth. There are plenty of ways to use fmincon to try to search for a global minimum, but NONE are guaranteed to find one in general. See the recent question https://www.mathworks.com/matlabcentral/answers/728568-how-to-know-if-a-minimum-found-with-global-search-is-actually-the-global-minimum?s_tid=srchtitle

Alan Weiss

MATLAB mathematical toolbox documentation

MATLAB: Optimization, fmincon. Help

Hi,

the usage of global variables is not recommended. You missed to define the function handles Fcost1_4 ... Fcost3_4 in Fcompanies_4.m - try this instead:

clc, clear all
global M H a1 a2 a3 b1 b2 b3 Lh umh u1h u2h u3h u4h Ch a4 Ge Ip
M=4;
H=24;
a1(1:7,1)=0.004;
a1(8:24,1)=0.00084;
a2(1:7,1)=0.0006;
a2(8:24,1)=0.00078;
a3(1:7,1)=0.0005;
a3(8:24,1)=0.00080;
b1(1:7,1)=0.064;
b1(8:24,1)=0.064;
b2(1:7,1)=0.046;
b2(8:24,1)=0.063;
b3(1:7,1)=0.044;
b3(8:24,1)=0.065;
r=0.09;
Ns=20;
a4= r/[1-(1+r)^-Ns];
Ge=1.6;
Ip=5000;
dv=H;
Lh=rand(1,H);
umh_i=rand(1,H*M);
u1h=umh_i(1,1:24);
u2h=umh_i(1,25:48);
u3h=umh_i(1,49:72);
u4h=umh_i(1,73:96);
current_m=1;
x0 = u1h;
ub = ones(dv,1);
lb = zeros(dv,1);
Fcost1_4 = @(x)globalfun(x);
Fcost2_4 = @(x)globalfun(x);
Fcost3_4 = @(x)globalfun(x);
options = optimoptions('fmincon','Algorithm','interior-point','Display','iter');
[x,fval] =fmincon(Fcost1_4,x0,[],[],[],[],lb,ub,[],options);
if(x~=u1h)
    u1h=x;
end
current_m=2;
x0=u2h;
ub=1-(u1h);
lb=zeros(dv,1);
options = optimoptions('fmincon','Algorithm','interior-point','Display','iter');
[x,fval] =fmincon(Fcost2_4,x0,[],[],[],[],lb,ub,[],options);
if(x~=u2h)
    u2h=x;
end
current_m=3;
x0=u3h;
ub=1-(u1h+u2h);
lb=zeros(dv,1);
options = optimoptions('fmincon','Algorithm','interior-point','Display','iter');
[x,fval] =fmincon(Fcost3_4,x0,[],[],[],[],lb,ub,[],options);
if(x~=u3h)
    u3h=x;
end
current_m=4;
u4h=1-(u1h+u2h+u3h);
[C]=F_final();
Ch=C;
umh=u1h+u2h+u3h+u4h;

In Fcost1.m your output is a function handle - try this instead:

function y = globalfun(x)
global M H a1 a2 a3 b1 b2 b3 Lh umh u1h u2h u3h
for h=1:H
y = (a1(h)*(Lh(h)*x(h)).^2 + b1(h)*(Lh(h)*x(h)) + a2(h)*(Lh(h)*u2h(h)).^2 + b2(h)*(Lh(h)*u2h(h)) + a3(h)*(Lh(h)*u3h(h)).^2 + b3(h)*(Lh(h)*u3h(h)));
end
end

These changes fix the code to run up to the last three lines:

[C]=F_final();

F_final is not defined - you should fix this and it should work. But you wil not get a price for clean coding... ;-)

In your globalfun you overwrite the result of y in every single run of your loop - i guess this is not what you want. Check the results - they may be not the expected ones, due to coding errros i cant identify, becaus of no insight to the problem.

Best regards

Stephan

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