Kim-Manuel Klein
Kim-Manuel Klein
We consider so called 2-stage stochastic integer programs (IPs) and their generalized form, so called multi-stage stochastic IPs. A 2-stage stochastic IP is an integer program of the form max { c T x ∣ A x = b , l ≤ x ≤ u...
Tim A Hartmann,Stefan Lendl,Gerhard J Woeginger
Tim A Hartmann
We study a continuous facility location problem on undirected graphs where all edges have unit length and where the facilities may be positioned on the vertices as well as on interior points of the edges. The goal is to cover the entire gra...
An optimal monotone contention resolution scheme for bipartite matchings via a polyhedral viewpoint [0.03%]
基于几何视角的二分图匹配的最优单调竞争解析方案
Simon Bruggmann,Rico Zenklusen
Simon Bruggmann
Relaxation and rounding approaches became a standard and extremely versatile tool for constrained submodular function maximization. One of the most common rounding techniques in this context are contention resolution schemes. Such schemes r...
Evan DeCorte,Fernando Mário de Oliveira Filho,Frank Vallentin
Evan DeCorte
We introduce the cone of completely positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a...
Samuel Fiorini,Tony Huynh,Stefan Weltge
Samuel Fiorini
In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist several general-purpose methods that strengthen relaxations without specific know...
Antoine Lagarde,Tristan Tomala
Antoine Lagarde
We consider the problem of optimal partisan gerrymandering: a legislator in charge of redrawing the boundaries of equal-sized congressional districts wants to ensure the best electoral outcome for his own party. The so-called gerrymanderer ...
Tikhonov regularization of a second order dynamical system with Hessian driven damping [0.03%]
由Hessian驱动阻尼的二阶动力系统的Tikhonov正则化
Radu Ioan Boţ,Ernö Robert Csetnek,Szilárd Csaba László
Radu Ioan Boţ
We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilb...
Stochastic quasi-gradient methods: variance reduction via Jacobian sketching [0.03%]
随机拟梯度方法：通过雅可比素描减少方差
Robert M Gower,Peter Richtárik,Francis Bach
Robert M Gower
We develop a new family of variance reduced stochastic gradient descent methods for minimizing the average of a very large number of smooth functions. Our method-JacSketch-is motivated by novel developments in randomized numerical linear al...
Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrieval [0.03%]
随机初始化的梯度下降：非凸相位检索的快速全局收敛性
Yuxin Chen,Yuejie Chi,Jianqing Fan et al.
Yuxin Chen et al.
This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest x ♮ ∈ ℝ n from m quadratic equations/samples y i = ( a i ⊤ x ♮ ) 2 , 1 ≤ i Ͱ...
Yurii Nesterov
Yurii Nesterov
In this paper we develop new tensor methods for unconstrained convex optimization, which solve at each iteration an auxiliary problem of minimizing convex multivariate polynomial. We analyze the simplest scheme, based on minimization of a r...