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.

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 applies the ...

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 ...

A new gradient-based neural network is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory, and LaSalle invariance principle to solve ...