This paper presents a new solution technique for the traffic assignment problem. The approach is based on an iteratively improved nonlinear and separable approximation of the originally nonseparable objective function, and resembles the Frank-Wolfe algorithm in the sense that the subproblem separates with respect to commodities. Since the singlecommodity subproblems are strictly convex, the new...

This article combines techniques from two fields of applied mathematics: optimization theory and inverse problems. We investigate the equivalence of the classical conditional gradient method and the surrogate method, which has been recently proposed for solving inverse problems. The method of surrogate functionals aims at the solution of non-quadratic minimization problems where the solution is...

As a starting point of this paper we present a problem from mammographic image processing. We show how it can be formulated as an optimal control problem for PDEs and illustrate that it leads to penalty terms which are non-standard in the theory of optimal control of PDEs. To solve this control problem we use a generalization of the conditional gradient method which is especially suitable for n...

In this paper we consider optimization problems de ned by a quadratic objective function and a nite number of quadratic inequality constraints. Given that the objective function is bounded over the feasible set, we present a comprehensive study of the conditions under which the optimal solution set is nonempty, thus extending the so-called Frank-Wolfe theorem. In particular, we rst prove a gene...

We introduce an algorithm, based on the Frank-Wolfe technique (conditional gradient), for performing marginal inference in undirected graphical models by repeatedly performing MAP inference. It minimizes standard Bethe-style convex variational objectives for inference, leverages known MAP algorithms as black boxes, and offers a principled means to construct sparse approximate marginals for high...

We present a new primal-dual algorithm for computing the value of the Lagrangian 6 dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity con7 straints. The algorithm relies on the well-known progressive hedging method, but unlike previous 8 progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal 9 Lagrangian dual value....

We introduce a globally-convergent algorithm for optimizing the tree-reweighted (TRW) variational objective over the marginal polytope. The algorithm is based on the conditional gradient method (Frank-Wolfe) and moves pseudomarginals within the marginal polytope through repeated maximum a posteriori (MAP) calls. This modular structure enables us to leverage black-box MAP solvers (both exact and...

In this work, we propose an infinite restricted Boltzmann machine (RBM), whose maximum likelihood estimation (MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each iteration, so that the optimization process takes the form of a sequence of fini...

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW optimization, we provide the first proof of convergence of a FW-type saddle point solver over polytopes, thereby partially answering a 30 year-old conjecture. We a...

We study parallel and distributed Frank-Wolfe algorithms; the former on shared memory machines with mini-batching, and the latter in a delayed update framework. In both cases, we perform computations asynchronously whenever possible. We assume block-separable constraints as in Block-Coordinate Frank-Wolfe (BCFW) method (Lacoste-Julien et al., 2013), but our analysis subsumes BCFW and reveals pr...