The spectral k-support norm enjoys good estimation properties in low rank matrix learning problems, empirically outperforming the trace norm. Its unit ball is the convex hull of rank k matrices with unit Frobenius norm. In this paper we generalize the norm to the spectral (k, p)support norm, whose additional parameter p can be used to tailor the norm to the decay of the spectrum of the underlyi...

We investigate the problem of Lp-norm constrained coding, i.e. converting signal into code that lies inside the Lp-ball and most faithfully reconstructs the signal. While previous works known as sparse coding have addressed the cases of `0 "norm" and L1-norm, more general cases with other p values, especially with unknown p, remain a difficulty. We propose the Frank-Wolfe Network (F-W Net), who...

In this paper, the accelerated Chambolle projection algorithms based on Frank–Wolfe have been proposed. For solving image restoration under additive Gaussian noise, method (CP) is widely used. However, operator has a large computational cost and complex form. By means of method, operation can be greatly simplified. We propose two new algorithms, called (CP–FW) (CP–AFW). They fast convergence ra...

In this paper, we consider the application of several gradient methods to traffic assignment problem: search equilibria in stable dynamics model (Nesterov and De Palma, 2003) Beckmann model. Unlike celebrated Frank–Wolfe algorithm widely used for model, these gradients solve dual problem then reconstruct a solution primal one. We deal with universal method, method similar triangles, weighted av...

Discrete network design is an important part of urban transportation planning. The purpose of this paper is to present a bilevel model for discrete network design. The upper-level model aims to minimize the total travel time under a stochastic demand to design a discrete network. In the lower-level model, demands are assigned to the network through a multiuser traffic equilibrium assignment. Ge...

Motivated by matrix recovery problems such as Robust Principal Component Analysis, we consider a general optimization problem of minimizing a smooth and strongly convex loss applied to the sum of two blocks of variables, where each block of variables is constrained or regularized individually. We present a novel Generalized Conditional Gradient method which is able to leverage the special struc...

The high computational cost of nonlinear support vector machines has limited their usability for large-scale problems. We propose two novel stochastic algorithms to tackle this problem. These algorithms are based on a simple and classic optimization method: the Frank-Wolfe method, which is known to be fast for problems with a large number of linear constraints. Formulating the nonlinear SVM pro...

We propose a Frank-Wolfe (FW) solver to optimize the symmetric nonnegative matrix factorization problem under a simplicial constraint. Compared with existing solutions, this algorithm is extremely simple to implement, and has almost no hyperparameters to be tuned. Building on the recent advances of FW algorithms in nonconvex optimization, we prove an O(1/ε) convergence rate to stationary points...