_phase_one(A, b, x0, callback, postsolve_args, maxiter, tol, disp, maxupdate, mast, pivot)
Generates an auxiliary problem with a trivial BFS and an objective that minimizes infeasibility of the original problem. Solves the auxiliary problem using the main simplex routine (phase two). This either yields a BFS to the original problem or determines that the original problem is infeasible. If feasible, phase one detects redundant rows in the original constraint matrix and removes them, then chooses additional indices as necessary to complete a basis/BFS for the original problem.
The purpose of phase one is to find an initial basic feasible solution (BFS) to the original problem.
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