相关论文: Dual Prices for Frank--Wolfe Algorithms

We investigate variants of the Frank-Wolfe (FW) algorithm for smoothing and strongly convex optimization over polyhedral sets, with the goal of designing algorithms that achieve linear convergence while minimizing per-iteration complexity…

This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with…

We consider the problem of a firm seeking to use personalized pricing to sell an exogenously given stock of a product over a finite selling horizon to different consumer types. We assume that the type of an arriving consumer can be observed…

Modern second order solvers for convex optimisation, such as interior point methods, rely on primal dual information and are difficult to warm start, limiting their applicability in real time control. We propose the PVM, a duality free…

We study the Frank-Wolfe algorithm for constrained optimization problems with relatively smooth objectives. Building upon our previous work, we propose a fully adaptive variant of the Frank-Wolfe method that dynamically adjusts the step…

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…

This paper presents a subgradient-based algorithm for constrained nonsmooth convex optimization that does not require projections onto the feasible set. While the well-established Frank-Wolfe algorithm and its variants already avoid…

This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…

In this paper, we consider large-scale linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose a scalable \textbf{F}rank-\textbf{W}olfe based…

Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…

This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…

We propose an algorithm which appears to be the first bridge between the fields of conditional gradient methods and abs-smooth optimization. Our problem setting is motivated by various applications that lead to nonsmoothness, such as…

We design accelerated algorithms with improved rates for several fundamental classes of optimization problems. Our algorithms all build upon techniques related to the analysis of primal-dual extragradient methods via relative Lipschitzness…

In this paper we consider distributed optimization problems in which the cost function is separable (i.e., a sum of possibly non-smooth functions all sharing a common variable) and can be split into a strongly convex term and a convex one.…

This study proposes an airborne multisensor management algorithm for target tracking, taking each of multiple unmanned aircraft as a sensor. The purpose of the algorithm is to determine the configuration of the sensor deployment and to…

This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a…

We propose Frank--Wolfe (FW) algorithms with an adaptive Bregman step-size strategy for smooth adaptable (also called: relatively smooth) (weakly-) convex functions. This means that the gradient of the objective function is not necessarily…

In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…

In this paper, we propose a generalized conditional gradient method for multiobjective optimization, which can be viewed as an improved extension of the classical Frank-Wolfe (conditional gradient) method for single-objective optimization.…

Learning a deep neural network requires solving a challenging optimization problem: it is a high-dimensional, non-convex and non-smooth minimization problem with a large number of terms. The current practice in neural network optimization…