dual simplex algorithm

The dual simplex algorithm is a method used in optimization to find the best solution when some but not all constraints are initially satisfied. Instead of starting with a feasible solution, it begins with a solution that may violate some constraints on the primal side but satisfies the dual constraints. The algorithm then systematically adjusts variables to improve the solution, maintaining dual feasibility, until a primal feasible and optimal solution is found. Essentially, it works by fixing infeasibilities in constraints efficiently, making it useful for problems where the initial feasible solution is difficult to identify.