Constrained Optimization of Implicitly Defined Function

Is there an algorithm in Matlab for the type of problem I present below?

Implicitly defined function y is to be optimized in an nx1 vector x, subject to linear constraints on x:

max y(x): p(1)*exp(r(1)/y) + ... + p(n)*exp(r(n)/y) - 1 = 0;

such that

     x'*ones(n,1) = 1;
     x'*r = c;

where mx1 vector p is given, c is given constant, and mx1 vector r=A*x; where A is a given mxn matrix

Answer 1

[Torsten]

Sure. Use "fmincon" to solve

max y

s.t.

p(1)*exp(r(1)/y) + ... + p(n)*exp(r(n)/y) - 1 = 0
x'*ones(n,1) = 1
x'*A*x = c

But A has to be an (nxn) matrix !

Best wishes

Torsten.

[X. Wu]

I am dealing with the same question. My objective function is also y as a implicit function of x. I am not sure how I should write the code using fmincon.

Wish to hear your suggestions.