Minimizing a function

    function [w_min value] = minimize(w0,H)
        [w_min value] = fminsearch(@(w) funtomini(w,H,w0) , w0);
    end
    function value = funtomini(w,H,w0)
        if sum(abs(w))<3; 
            value = w'*H*w;
        else
            value = w0'*H*w0;
        end
    end

Find the minimum using this command

[w_min value] = minimize(w0,H);

Cheers,

Cédric

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Answer 2

Teja Muppirala 2011-9-7

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https://ww2.mathworks.cn/matlabcentral/answers/15218-minimizing-a-function#answer_20723

在 MATLAB Online 中打开

This is a quadratic programming problem, and can be solved very easily using QUADPROG. The only thing is correctly expressing the L1 constraint.

% Make some random H
H = rand(3,3);
H =H+H';
% Express the L1 constraint using matrices:
[X1,X2,X3] = ndgrid([-1 1]);
A = [X1(:) X2(:) X3(:)];
b = 3*ones(size(A,1),1);
% solve for x
x = quadprog(H,[],A,b)

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Jen 2011-9-8

This method is correct, however when I applied to to my problem where N =25, I run out of memory.

I get the following error:

??? Error using ==> horzcat

Out of memory. Type HELP MEMORY for your options.

Error in ==> GMVPC1Type3 at 6

A = [X1(:) X2(:) X3(:) X4(:) X5(:) X6(:) X7(:) X8(:) X9(:) X10(:) X11(:) X12(:) X13(:) X14(:)

X15(:) X16(:) X17(:) X18(:) X19(:) X20(:) X21(:) X22(:) X23(:) X24(:) X25(:)];

Error in ==> SCM12 at 63

PortfolioWeights = GMVPC1Type3(SCM);

Do you have any other suggestions?

Jen 2011-9-8

The fmincon code works below for some matrices, but for other, gives equal weights to w1,w2 and w3. Any ideas why this is?

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Answer 3

Jen 2011-9-7

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/15218-minimizing-a-function#answer_20754

在 MATLAB Online 中打开

Cedric - Will give it a go

Teja - I initially used QUADPROG, but couldnt find a way of expressing the L1 constraint.

I decided to use fmincon with a nonlinear constraint.

Aeq = [1,1,1;0.05,0.06,0];
beq = [1;0.05];
A = [0,1,0];
b = 0.5;
w0 = [0.5 0.5 0.5];
[w,fval] = fmincon(@myobj,w0,A,b,Aeq,beq,[],[],@myconstraint)
------------------------------------------------------------------
function f = myobj(w)
diagmatrix = [0.15,0,0;0,0.20,0;0,0,0.40];
corrmatrix = [1,0.5,-0.7;0.5,1,-0.4;-0.7,-0.4,1];
covmatrix = diagmatrix*corrmatrix*diagmatrix;
w = [w(1);w(2);w(3)];
f = w'*covmatrix*w;
end
-----------------------------------------------------------------
function [c ceq] = myconstraint(w)
c = abs(w(1)) + abs(w(2)) + abs(w(3))-3;
ceq = [];
end
------------------------------------------------------------------