Find interior point in a convex polygon with min 'z' with CVXOPT

[Jayanth Mondi]

HI all,

Can I solve the problem of finding a point in the convex polygon with a minimum value of objective function?

I have the information of the various vertices (n-dimensional) of the convex polygon created by projecting onto a chosen 2D plane.

Thanks,
Jayanth

[Martin]

Yes, if the objective function is convex. You can represent the feasible set as a convex combination of the vertices, i.e., if V is a matrix where each column corresponds to a vertex, then your problem can be expressed as follows:

   minimize f(x) 

   subject to  x = V*y,  sum(y) == 1,  y>=0