the problem of finding the minimum cost multi-commodity flow in an undirected and completenetwork is studied when the link costs are piecewise linear and convex. the arc-path model and overflowmodel are presented to formulate the problem. the results suggest that the new overflow model outperformsthe classical arc-path model for this problem. the classical revised simplex, frank and wolf and a ...

We present versions of the Frank-Wolfe method for linearly constrained convex programs, in which consecutive search directions are made conjugate. Preliminary computational studies in a MATLAB environment applying pure Frank-Wolfe, Conjugate direction Frank-Wolfe (CFW), Bi-conjugate Frank-Wolfe (BFW) and ”PARTANized” Frank-Wolfe methods to some classical Traffic Assignment Problems show that CF...

In this paper, we describe a new active-set algorithmic framework for minimizing a function over the simplex. The method is quite general and encompasses different active-set Frank-Wolfe variants. In particular, we analyze convergence (when using Armijo line search in the calculation of the stepsize) for the active-set versions of standard Frank-Wolfe, away-step Frank-Wolfe and pairwise Frank-W...

We propose a rank-k variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball. Our algorithm replaces the top singular-vector computation (1-SVD) in Frank-Wolfe with a top-k singular-vector computation (k-SVD), which can be done by repeatedly applying 1-SVD k times. Our algorithm has a linear convergence rate when the objective function is smooth and str...

Abstract Invented some 65 years ago in a seminal paper by Marguerite Straus-Frank and Philip Wolfe, the Frank–Wolfe method recently enjoys remarkable revival, fuelled need of fast reliable first-order optimization methods Data Science other relevant application areas. This review tries to explain success this approach illustrating versatility applicability wide range contexts, combined with an ...

In this paper, we are concerned with minimization problems over the unit simplex. Here, we propose the use of an active-set estimate that enables us to define an algorithmic framework where the variables estimated active and those estimated non-active are updated separately at each iteration. In particular, we consider different variants of the Frank-Wolfe direction to be combined with the prop...

We present new results for the Frank-Wolfe method (also known as the conditional gradient 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 (...

The paper is inspired by the stress-strength models in the reliability literature, in which given the strength (Y ) and the stress (X) of a component, its reliability is measured by P (X < Y ). In this literature, X and Y are typically modeled as independent. Since in many applications such an assumption might not be realistic, we propose a copula approach in order to take into account the depe...

We propose a novel partial linearization based approach for optimizing the multi-class svm learning problem. Our method is an intuitive generalization of the Frank-Wolfe and the exponentiated gradient algorithms. In particular, it allows us to combine several of their desirable qualities into one approach: (i) the use of an expectation oracle (which provides the marginals over each output class...