DDS Users' Guide

Hyperbolic Optimization

Consider a hyperbolic polynomial constraint of the form \begin{eqnarray} \label{eq:hyper-4} % p(Ax+b) \leq 0, \ \ i \in \{1,\ldots,\ell\}. p(Ax+b) \geq 0. \end{eqnarray} To input this constraint to DDS as the \(k\)th block, \(A\) and \(b\) are defined as before, and different parts of cons are defined as follows:

cons{k,1}='HB' ,
cons{k,2}= number of variables in \(p(x)\).
cons{k,3} is the polynomial matrix poly that can be given as one of the three formats.
cons{k,4} is the format of polynomial that can be 'monomial, 'straight_line', or 'determinant'.
cons{k,5} is the direction of hyperbolicity or a vector in the interior of the hyperbolicity cone.

For seeing the details and also the three different formats of giving a polynomial as input, please see the user's guide .