We provide Frank-Wolfe (≡ Conditional Gradients) method with a convergence analysis allowing to approach a primal-dual solution of convex optimization problem with composite objective function. Additional properties of complementary part of the objective (strong convexity) significantly accelerate the scheme. We also justify a new variant of this method, which can be seen as a trust-region sche...

We consider convex optimization problems which are widely used as relaxations for low-rank matrix recovery problems. In particular, in several important problems, such phase retrieval and robust PCA, the underlying assumption many cases is that optimal solution rank-one. this paper we a simple natural sufficient condition on objective so to these indeed unique Mainly, show under condition, stan...

We describe a branch and bound algorithm for the quadratic assignment problem QAP that uses a convex quadratic programming QP relaxation to obtain a bound at each node The QP subproblems are approximately solved using the Frank Wolfe algorithm which in this case requires the solution of a linear assignment problem on each iteration Our branching strategy makes extensive use of dual information ...

Estimating the most likely configuration (MAP) is one of the fundamental tasks in probabilistic models. While MAP inference is typically intractable for many real-world applications, linear programming relaxations have been proven very effective. Dual block-coordinate descent methods are among the most efficient solvers, however, they are prone to get stuck in sub-optimal points. Although subgr...

Recently, research on accelerated stochastic gradient descentmethods (e.g., SVRG) has made exciting progress (e.g., lin-ear convergence for strongly convex problems). However,the best-known methods (e.g., Katyusha) requires at leasttwo auxiliary variables and two momentum parameters. Inthis paper, we propose a fast stochastic variance reductiongradient (FSVRG) method...