0-penalized problems arise in a number of applications in engineering, machine learning and statistics, and, in the last decades, the design of algorithms for these problems has attracted the interest of many researchers. In this paper, we are concerned with the definition of a first-order method for the solution of 0-penalized problemswith simple constraints.Weuse a reduced dimension Frank–Wol...

With the well-documented popularity of Frank Wolfe (FW) algorithms in machine learning tasks, present paper establishes links between FW subproblems and notion momentum emerging accelerated gradient methods (AGMs). On one hand, these reveal why is unlikely to be effective for FW-type on general problems. other it established that accelerates a class signal processing applications. Specifically,...

We study a natural generalization of the knapsack problem, in which each item exists only for a given time interval. One has to select a subset of the items (as in the classical case), guaranteeing that for each time instant the set of existing selected items has total weight not larger than the knapsack capacity. We focus on the exact solution of the problem, noting that prior to our work the ...

The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space costs for large problems. To address this issue, we propose a rank-drop method for nuclear norm constrained problems. The goal is to generate descent steps ...

2014 The existence of a critical thickness for a hybrid aligned nematic cell has been recently predicted on the basis of the Frank elasticity. The purpose of the present work is to show the dependence of the critical thickness on the surface-like volume elasticity and to find new limits for K13 in terms of the principal elastic constants. J. Physique Lett. 45 (1984) L-857 L-862 ler SEPTEMBRE 19...

We give a simple proof that the Frank-Wolfe algorithm obtains a stationary point at a rate of O(1/ √ t) on non-convex objectives with a Lipschitz continuous gradient. Our analysis is affine invariant and is the first, to the best of our knowledge, giving a similar rate to what was already proven for projected gradient methods (though on slightly different measures of stationarity).

Covariate shift is a fundamental problem for learning in non-stationary environments where the conditional distribution ppy|xq is the same between training and test data while their marginal distributions ptrpxq and ptepxq are different. Although many covariate shift correction techniques remain effective for real world problems, most do not scale well in practice. In this paper, using inspirat...

We present new results for the conditional gradient method (also known as the Frank-Wolfe method). We derive computational guarantees for arbitrary step-size sequences, which are then applied to various step-size rules, including simple averaging and constant step-sizes. We also develop step-size rules and computational guarantees that depend naturally on the warm-start quality of the initial (...

Structured sparse estimation has become an important technique in many areas of data analysis. Unfortunately, these estimators normally create computational difficulties that entail sophisticated algorithms. Our first contribution is to uncover a rich class of structured sparse regularizers whose polar operator can be evaluated efficiently. With such an operator, a simple conditional gradient m...

We study the round complexity of minimizing the average of convex functions under a new setting of distributed optimization where each machine can receive two subsets of functions. The first subset is from a random partition and the second subset is randomly sampled with replacement. Under this setting, we define a broad class of distributed algorithms whose local computation can utilize both s...