Re: sqp -- global optimum if convex?

[dikdirk]

Apr 16, 2012; 9:34pm — by forkandwait forkandwait
>Does anyone know of any theorems on that sqp is guaranteed to converge to a
>global optimum if the objective function is convex (and constraint
functions are
>affine)?

>I want to dabble in entropy maximization (a convex objective) for some
>sociological applications, and it would be great if this were true.

>A reference would be great -- I can follow up in the local college library.

>Thx! 


I am also interested in more information about the algorithm behind sqp...
the documentation is a bit limited and only states the how to use sqp, but
not what kind of problems it supports.

Does anyone know whether there are any restriction on the objective function
or the constraints?

I already tested that if the objective function is not convex, then the
algorithm might converge to a local minimum. This answers forkandwait
question, see this example:

function y= constraint (x)
        y = x(2);
end

function y = toMinimize (x)
        y = (x(1) - 1)^2*(x(1) + 1)^2 + (x(1) - 1);
end

%global min at x(1)=-1, x(2)=0
x0=[-2,0];
[x_new, obj, info, iter, nf, lambda] = sqp (x0, @(x) toMinimize(x), @(x)
constraint (x), [],[],[],1000,1e-8)

%but the algorithm can get stuck in x(1)=1
x0=[3,0];
[x_new, obj, info, iter, nf, lambda] = sqp (x0, @(x) toMinimize(x), @(x)
constraint (x), [],[],[],1000,1e-8)



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