Optimization of a unknown vector variable

Hello ,

I have a code

a,b -----> variables should be vector(like a=[a1,a2,a3,a4])

x=h1*a^2+h2*b^2+h3;------>objctive fun(h1,h2,h3 are constants let say which has 1*4 value)

---->constraints are also present here.. so I am writting the code like

for i=1:4
x(i)=h1(i)*a^2+h2(i)*b^2+h3(i)
end
obj=sum(x);----->(objective function is basically summation of x )

x0=[1,1];
lb = [];
ub = [];
Aeq = [];
beq =[];
A = [];
b = [];
 fun=@(p) obj(p(1),p(2));
nonlcon =@constraintfcn;
opts = optimoptions('fmincon','Display','iter','Algorithm','sqp');
 [x_value,fval]  = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,opts);

But I am not getting the ans,I want optimized value as vector .

[Matt J]

Quite unclear, I'm afraid. What is the for-loop supposed to be doing? Do you have more than one objective to minimize? Why does the right hand side not depend on i?

[Soumili Sen]

yes, you are right. My objective function is summation of 'x' (I have modified my code), and the unknown optimized veriables are vector. so how can I continue to find the values?

Answer 1

[Matt J]

H1=sum(h1);
H2=sum(h2);
H3=sum(h3);

obj=@(a,b) H1.*a.^2 +H2.*b.^2+H3;

x0=[1,1];
lb = [];
ub = [];
Aeq = [];
beq =[];
A = [];
b = [];
 fun=@(p) obj(p(1),p(2));
nonlcon =@constraintfcn;
opts = optimoptions('fmincon','Display','iter','Algorithm','sqp');
 [x_value,fval]  = fmincon( fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,opts);

[Soumili Sen]

Thanks for response, but here we are getting a single value of a & b.like

x_value= 1.23,2.3 ---> (values of a and b corresponding)

but I want optimizd value as a=4 values(like a1,a2,a3,a4) and b=4 values.

here I am using unknown veriable declaration as

syms a b;

for my desire output can I write it like

a=sym('a',[1 4]);

If it possible,how can I further proceed?

[Matt J]

The objective function that you have shown us is only dependent on a single a and b. You have not shown us an 8 variable objective function.

[Soumili Sen]

ok.sorry for my mistake.how I can resolve this problem according to my desire output?

[Matt J]

You must show us the objective function that you really want. I still don't know what it is.

[John D'Errico]

As it is, with the objective function shown, the min lies at all zeros for the vector a, since the objective function is just a weighted sum of the squares of the elements in a. That assumes all the elements in h are non-negative. If any element of h is negative, then no minimum exists.

As Matt says, if this does not satisfy the problem (I doubt it will) then more information is needed.

[Soumili Sen]

ok, below I have modified the representation of my objective function,

h1=rand(1,4);
h2=rand(1,4);
h3=rand(1,4);
a=sym('a',[1 4]);
b=sym('b',[1 4]);

x=h1.*a+h2.*b+h3;
for i=1:4
x1(i)=norm(x(i));
end
obj=sum(x1)

How I can optimized this a values and b values? thanks in advance.

[Matt J]

Similar to fun() below, nonlcon must accept input in the form of a 4x2 matrix p.

 obj=@(a,b) dot(h1,a)+dot(h2,b)+sum(h3);

 fun=@(p) obj(p(:,1),p(:,2));

 [x_value,fval]  = fmincon(fun,ones(4,2),[],[],[],[],nonlcon,opts);

[Soumili Sen]

yah,the code is running. Thank you so much to clarify the doubts. I have one question i.e,

if I want complex value of 'a' (a,a2,a3,a4 are complex in nature) then how the code will be modified?

[Matt J]

If a=ar+ac*1i, then you must rewrite the problem with ar and ac (which are real-valued) as the unknowns.

[Soumili Sen]

ok,thanks

[Matt J]

You're welcome, but please Accept-click the answer if you consider the matter resolved.

[Soumili Sen]

yah sure.