How do i formulate the following otimization function in matlab?

min summation over i {y1*log(1+x(i))*x(i)/sum(x(i))-y2*x(i)}

The above problem has a summation inside a summation of the same variable.

can such functions be optimized for x(i) and y(j) using matlab solvers such as fmincon? is there and other solver that can optimize such objective functions with constraints.

Thank you

Answer 1

[Alan Weiss]

This is straightforward to formulate and solve using Optimization Toolbox solvers such as fmincon. However, I am not sure that I understand your problem exactly. Are y1 and y2 given, and you want to minimize over a vector x(1),...,x(n)? What kinds of constraints do you want to include?

For introductory examples using Optimization Toolbox, see a Getting Started example and a nonlinear data fitting example.

Alan Weiss

MATLAB mathematical toolbox documentation

[Kane0610]

y(j) are the variables along with the x(i)s.(they are not given).Also the constraint are nonlinear but convex. The objective function too is convex.