Find (if possible) an interior point of a polytope solving a linear program
witness(A, b, s, epsbound = 1, epstol = 1e-07, presolve = 1, verb = 0)
List with components:
w proposed interior point at solution
fail indicator of whether w is a valid interior point
Is a n by d matrix of hyperplane slope coefficients.
Is an n vector of hyperplane intercept coefficients.
Is an n vector of signs.
Is a scalar tolerance controlling how close the witness point can be to an edge of the polytope.
Is a scalar tolerance for the LP convergence.
Controls whether Mosek should presolve the LP.
Controls verbosity of Mosek solution.
Solves LP: \(max over {w,eps} {eps | SAw - eps >= Sb, 0 < eps <= epsbound}\) S is diag(s), if at the solution eps > 0, then w is a valid interior point otherwise the LP fails to find an interior point, another s must be tried. Constructs a problem formulation that can be passed to Rmosek for solution.