A Primal-Dual Frank-Wolfe Algorithm for Linear Programming


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 Frank-Wolfe algorithm to both the primal and dual of the saddle point formulation of a standard-form LP. The latter is a modification of FWLP in which regularizing perturbations are used in computing the iterates. We show that FWLP-P converges to a primal-dual solution with error O(1/sqrt(k)) after k iterations, while no convergence guarantees are provided for FWLP. We also discuss the advantages of using FWLP and FWLP-P for solving very large LPs. In particular, we argue that only part of the matrix A is needed at each iteration, in contrast to other first-order methods.


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