The dual simplex method, unlike the standard simplex method, starts with an infeasible but optimal (or better) solution for the objective function in a linear programming problem.

Abstract: We present two first-order primal-dual algorithms for solving saddle point formulations of linear programs, namely FWLP (Frank-Wolfe Linear Programming) and FWLP-P. The former iteratively ...

The multiobjective bilevel linear programming (MBLP) is a hierarchical optimization problem involving two levels, and at least one level has multiple objectives. This paper mainly studies a special ...

For linear programming and quadratic programming (QP) problems with unique and infinite number of solutions, we have proven strictly that for any initial point, every trajectory of the neural network ...

However, standard FOMs, such as the primal-dual hybrid gradient (PDHG) method, are not yet reliable for LP problems, solving only a small fraction of instances. Google researchers introduce PDLP ...