Conditional gradient algorithms (aka Frank–Wolfe algorithms) form a classical set of methods for constrained smooth convex minimization due to their simplicity, the absence projection steps, and competitive numerical performance. While vanilla algorithm only ensures worst-case rate $${\mathcal {O}}(1/\epsilon )$$ , various recent results have shown that strongly functions on polytopes, method c...

We provide a self-contained convergence proof in this section. The skeleton of our convergence proof follow closely from Lacoste-Julien et al. (2013) and Jaggi (2013). There are a few subtle modification and improvements that we need to add due to our weaker definition of approximate oracle call that is nearly correct only in expectation. The delayed convergence is new and interesting for the b...

In this paper, we tackle the problem of performing efficient co-localization in images and videos. Co-localization is the problem of simultaneously localizing (with bounding boxes) objects of the same class across a set of distinct images or videos. Building upon recent stateof-the-art methods, we show how we are able to naturally incorporate temporal terms and constraints for video co-localiza...

Decentralized optimization algorithms have received much attention due to the recent advances in network information processing. However, conventional decentralized algorithms based on projected gradient descent are incapable of handling high dimensional constrained problems, as the projection step becomes computationally prohibitive to compute. To address this problem, this paper adopts a proj...

Algorithm 3 details the process for incrementally computing term (13) for all xk. (The process for computing (14) is similar.) Computation of the full gradient is thus also an O(nm) operation. Using this technique, we can apply full-gradient first-order methods efficiently, including gradient projection and Frank-Wolfe. With an appropriate line-search method, gradient projection is guaranteed t...

Aiming at convex optimization under structural constraints, this work introduces and analyzes a variant of the Frank Wolfe (FW) algorithm termed ExtraFW. The distinct feature ExtraFW is pair gradients leveraged per iteration, thanks to which decision variable updated in prediction-correction (PC) format. Relying on no problem dependent parameters step sizes, convergence rate for general problem...

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain variable, which are difficult to project onto; and (b) or that admit efficient projection. Problems this form arise frequently in context semidefinite programming as well when various NP-hard solved approximately via relaxation. Since projection onto first set i...