Minimization of function. Plz Help.

Maybe it can be easy, but please help. I am beginner in humble country.

R = (0.1 0 0.3;-0.2 -0.5 -0.1;0.15 0.2 -0.1]; (it can be changed)

[row,cols]=size( R );

f=ones(1,cols);

growth(R,f);

saved function to growth.m is

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function g = growth(R, f)

[ro,co] = size( R );

T = R*0.01/0.15;

g = -sum(log(1+T(1:ro,:)*f'))/ro;

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How can I minimize growth(R,f) with f(with given R)? Constraint is f1+|f2|+...+|fn|<=1

I want to iterate f=(f1,f2,f3,...,fn) like

f1=-1:0.01:1

f2=-1:0.01:1

f3=-1:0.01:1

...

Please help. very Thanks.

Answer 1

[Matt Tearle]

R = [1 2 3;4 5 6;7 8 9];
[row,cols] = size(R); 
f = ones(1,cols); 

fobj = @(x) growth(R,x);
opts = optimset('Algorithm','interior-point');
f = fmincon(fobj,f,[],[],[],[],[],[],@growthconstraints,opts)

This performs a constrained optimization on fobj which is growth(R,f) with R fixed (ie so a function of just f). The constraint is specified in growthconstraint.m:

function [c,ceq] = growthconstraints(x)
c = norm(x,1)-1;
ceq = 0;

This defines an inequality constraint (sum(f_j) <= 1) and a null equality constraint.

Answer 2

[the cyclist]

Do you have the Optimization Toolbox? The function fmincon() will do what you want.