Generalized Linear Programming Solves the Dual

Generalized Dual Face Algorithm for Linear Programming

As a natural extension of the dual simplex algorithm, the dual face algorithm performed remarkably in computational experiments with a set of Netlib standard problems. In this paper, we generalize it to bounded-variable LP problems via local duality.

Randomized Linear Programming Solves the Discounted Markov Decision Problem In Nearly-Linear (Sometimes Sublinear) Run Time

We propose a novel randomized linear programming algorithm for approximating the optimal policy of the discounted Markov decision problem. By leveraging the value-policy duality and binary-tree data structures, the algorithm adaptively samples state-action-state transitions and makes exponentiated primal-dual updates. We show that it finds an -optimal policy using nearly-linear run time in the ...

Randomized Linear Programming Solves the Discounted Markov Decision Problem In Nearly-Linear Running Time

We propose a novel randomized linear programming algorithm for approximating the optimal policy of the discounted Markov decision problem. By leveraging the value-policy duality and binary-tree data structures, the algorithm adaptively samples state-action-state transitions and makes exponentiated primal-dual updates. We show that it finds an ǫ-optimal policy using nearly-linear run time in the...

Dual Generalized Bases in Linear Topological Spaces

Primal-Dual Enumeration for Multiparametric Linear Programming

Optimal control problems for constrained linear systems with a linear cost can be posed as multiparametric linear programs (pLPs) and solved explicitly offline. Several algorithms have recently been proposed in the literature that solve these pLPs in a fairly efficient manner, all of which have as a base operation the computation and removal of redundant constraints. For many problems, it is th...