Owing to their low-complexity iterations, FrankWolfe (FW) solvers are well suited for various large-scale learning tasks. When block-separable constraints are present, randomized block FW (RB-FW) has been shown to further reduce complexity by updating only a fraction of coordinate blocks per iteration. To circumvent the limitations of existing methods, the present work develops step sizes for R...

Proof. Consider the function class F = {f(·,x) | x ∈ P} as defined in (SP1), that is f(i,x) = fi(x). Since fi(·) each is assumed to be Lipschitz continuous with Lipschitz constant Li, we must have |fi(x)− fi(y)| ≤ LF ‖x− y‖, where LF ≡ max{L1, . . . , Ln}. Moreover, the index set P ∈ R for the function class F is assume to be bounded. Therefore all conditions for Lemma 2 are satisfied and hence...

We provide stronger and more general primal-dual convergence results for FrankWolfe-type algorithms (a.k.a. conditional gradient) for constrained convex optimization, enabled by a simple framework of duality gap certificates. Our analysis also holds if the linear subproblems are only solved approximately (as well as if the gradients are inexact), and is proven to be worst-case optimal in the sp...

Training a Support Vector Machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be directly applied in these cases, mainly due to memory restrictions. By adopting a slightly different objective function and under mild conditions on the kernel use...

We present FrankWolfe.jl, an open-source implementation of several popular Frank–Wolfe and conditional gradients variants for first-order constrained optimization. The package is designed with flexibility high performance in mind, allowing easy extension relying on few assumptions regarding the user-provided functions. It supports Julia’s unique multiple dispatch feature, it interfaces smoothly...

This paper is concerned with the robust control problem of LFT (Linear Fractional Representation) uncertain systems depending on a time-varying parameter uncertainty. Our main result exploits an LMI (Linear Matrix Inequality) characterization involving scalings and Lya-punov variables subject to an additional essentially non-convex algebraic constraint. The non-convexity enters the problem in t...

Intersection left-turning restriction is one of the important ways to solving the road congestion of the builtup area; however, how to set scientifically and rationally is the key. A bi-level programming model was making under the minimum the premise entire traffic network access time by using the stochastic traffic assignment model which is more appropriate. The upper planning described the in...