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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：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...
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作者：Bungert, Leon; Roith, Tim; Wacker, Philipp
作者单位：University of Wurzburg; Helmholtz Association; Deutsches Elektronen-Synchrotron (DESY); University of Canterbury
摘要：In this paper we propose polarized consensus-based dynamics in order to make consensus-based optimization (CBO) and sampling (CBS) applicable for objective functions with several global minima or distributions with many modes, respectively. For this, we polarize the dynamics with a localizing kernel and the resulting model can be viewed as a bounded confidence model for opinion formation in the presence of common objective. Instead of being attracted to a common weighted mean as in the origina...
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作者：Burer, Samuel
作者单位：University of Iowa
摘要：Globally optimizing a nonconvex quadratic over the intersection of m balls in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>n$$\end{document} is known to be polynomial-time solvable for fixed m. Moreover, when m=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{a...
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作者：Harks, Tobias; Schwarz, Julian
作者单位：University of Passau
摘要：We consider generalized Nash equilibrium problems (GNEPs) with non-convex strategy spaces and non-convex cost functions. This general class of games includes the important case of games with mixed-integer variables for which only a few results are known in the literature. We present a new approach to characterize equilibria via a convexification technique using the Nikaido-Isoda function. To any given instance of the GNEP, we construct a set of convexified instances and show that a feasible st...
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作者：Poremba, Joseph; Shepherd, F. Bruce
作者单位：University of British Columbia
摘要：In multicommodity network flows, a supply-demand graph pair (G, H) (called a multiflow topology) is cut-sufficient if, for all capacity and demand weights, the cut condition is enough to guarantee the existence of a feasible multiflow. We characterize cut-sufficiency for two classes of directed 2-commodity flows: roundtrip demands, where H is a 2-cycle, and 2-path demands, where H is a directed path of length two. We then extend these characterizations to some larger demand graphs, namely dire...
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作者：Abdi, Ahmad; Cornuejols, Gerard; Guenin, Bertrand; Tuncel, Levent
作者单位：University of London; London School Economics & Political Science; Carnegie Mellon University; University of Waterloo
摘要：A rational number is dyadic if it has a finite binary representation p/2k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p/2<^>k$$\end{document}, where p is an integer and k is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in floating-poin...
