Find witness point
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)
A |
Is a n by d matrix of hyperplane slope coefficients. |
b |
Is an n vector of hyperplane intercept coefficients. |
s |
Is an n vector of signs. |
epsbound |
Is a scalar tolerance controlling how close the witness point can be to an edge of the polytope. |
epstol |
Is a scalar tolerance for the LP convergence. |
presolve |
Controls whether Mosek should presolve the LP. |
verb |
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.
List with components:
w proposed interior point at solution
fail indicator of whether w is a valid interior point
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