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作者：Zhang, Penghe; Xiu, Naihua; Qi, Houduo
作者单位：Hong Kong Polytechnic University; Beijing Jiaotong University; Hong Kong Polytechnic University; Hong Kong Polytechnic University
摘要：Indicator functions of taking values of zero or one are essential to numerous applications in machine learning and statistics. The corresponding primal optimization model has been researched in several recent works. However, its dual problem is a more challenging topic that has not been well addressed. One possible reason is that the Fenchel conjugate of any indicator function is finite only at the origin. This work aims to explore the dual optimization for the sum of a strongly convex functio...
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作者：Hubert, Evelyne; Metzlaff, Tobias; Moustrou, Philippe; Riener, Cordian
作者单位：Universite Cote d'Azur; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Toulouse - Jean Jaures; UiT The Arctic University of Tromso
摘要：We provide a new approach to the optimization of trigonometric polynomials with crystallographic symmetry. This approach widens the bridge between trigonometric and polynomial optimization. The trigonometric polynomials considered are supported on weight lattices associated to crystallographic root systems and are assumed invariant under the associated reflection group. On one hand the invariance allows us to rewrite the objective function in terms of generalized Chebyshev polynomials of the g...
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作者：Mathieu, Claire; Zhou, Hang
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：In the unsplittable capacitated vehicle routing problem (UCVRP) on trees, we are given a rooted tree with edge weights and a subset of vertices of the tree called terminals. Each terminal is associated with a positive demand between 0 and 1. The goal is to find a minimum length collection of tours starting and ending at the root of the tree such that the demand of each terminal is covered by a single tour (i.e., the demand cannot be split), and the total demand of the terminals in each tour do...
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作者：Zhang, Junyu
作者单位：National University of Singapore
摘要：We investigate stochastic Bregman proximal gradient (SBPG) methods for minimizing a finite-sum nonconvex function Psi(x):=1n & sum;i=1nfi(x)+phi(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Psi (x):=\frac{1}{n}\sum _{i=1}<^>nf_i(x)+\phi (x)$$\end{document}, where phi\documentclass[12pt]{minimal} \usepackage{a...
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作者：Bennouna, Amine; Van Parys, Bart P. G.
作者单位：Northwestern University; Massachusetts Institute of Technology (MIT); Centrum Wiskunde & Informatica (CWI)
摘要：We study the problem of designing optimal learning and decision-making formulations when only historical data is available. Prior work typically commits to a particular class of data-driven formulation and subsequently tries to establish out-of-sample performance guarantees. Following (Van Parys et al. From data to decisions: Distributionally robust optimization is optimal. Management Science 2020) we take here the opposite approach. We define first a sensible yardstick with which to measure t...
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作者：Dussault, Jean-Pierre; Frappier, Mathieu; Gilbert, Jean Charles
作者单位：University of Sherbrooke; University of Sherbrooke
摘要：The semismooth Newton method is a very efficient approach for computing a zero of a large class of nonsmooth equations. When the initial iterate is sufficiently close to a regular zero and the function is strongly semismooth, the generated sequence converges quadratically to that zero, while the iteration only requires to solve a linear system. If the first iterate is far away from a zero, however, it is difficult to force its convergence using linesearch or trust regions because a semismooth ...
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作者：Huang, Kun; Pu, Shi; Nedic, Angelia
作者单位：The Chinese University of Hong Kong, Shenzhen; Arizona State University; Arizona State University-Tempe
摘要：In this paper, we introduce an accelerated distributed stochastic gradient method with momentum for solving the distributed optimization problem, where a group of n agents collaboratively minimize the average of the local objective functions over a connected network. The method, termed Distributed Stochastic Momentum Tracking (DSMT), is a single-loop algorithm that utilizes the momentum tracking technique as well as the Loopless Chebyshev Acceleration (LCA) method. We show that DSMT can asympt...
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作者：Hirai, Hiroshi; Iwamasa, Yuni; Oki, Taihei; Soma, Tasuku
作者单位：Nagoya University; Kyoto University; Hokkaido University; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
摘要：We address the computation of the degrees of minors of a noncommutative symbolic matrix of form A[c]:=& sum;k=1mAktckxk,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ A[c] :=\sum _{k=1}<^>m A_k t<^>{c_k} x_k, $$\end{document}where Ak\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepacka...
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作者：Zhang, Richard Y.
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：If a sparse semidefinite program (SDP), specified over n x n matrices and subject to m linear constraints, has an aggregate sparsity graph G with small treewidth, then chordal conversion will sometimes allow an interior-point method to solve the SDP in just O(m + n) time per-iteration, which is a significant speedup over the Omega(n(3)) time per-iteration for a direct application of the interior-point method. Unfortunately, the speedup is not guaranteed by an O(1) treewidth in G that is indepe...
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作者：Benko, Matus; Mehlitz, Patrick
作者单位：University of Vienna; Philipps University Marburg
摘要：As a starting point of our research, we show that, for a fixed order gamma >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma \ge 1$$\end{document}, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to sta...
