Dual revised simplex with a finite pivot budget

Input the exact standard-form data and a basis $B$ for which every nonbasic reduced cost is nonnegative, as in Revised simplex standard-form linear program and Basis dictionaries and reduced costs for revised simplex. Also input a nonnegative integer pivot budget $K$. Set $k=0$ and repeat:

1. Compute $x_B=A_B^{-1}b$ and $y=A_B^{-\mathsf{T}}{c}_B$. If $x_B\ge 0$, return optimal with the primal basic vector and $y$.
2. Otherwise choose the least-index basic variable $B_i$ with $x_{B_i}<0$. For each nonbasic $j$ compute $d_{ij}=(A_B^{-1}{a}_j{)}_i$. If no $d_{ij}<0$, return infeasible with $q=A_B^{-\mathsf{T}}{e}_i$.
3. If $k=K$, return pivot-budget-exhausted with the current basis and multiplier $y=A_B^{-\mathsf{T}}{c}_B$.
4. Among $j$ with $d_{ij}<0$, choose one minimizing ${\bar{c}}_j\mathrm{/}(-d_{ij})$, with least variable index among ties. Replace $B_i$ by $j$, set $k\leftarrow k+1$, and repeat.

The pivot-budget-exhausted status is inconclusive. No finite-success or anti-cycling claim is part of this definition.