2024

最新文章

• A single cut proximal bundle method for stochastic convex composite optimization AI翻译
  作者：Liang, Jiaming; Guigues, Vincent; Monteiro, Renato D. C.
  作者单位：University of Rochester; University of Rochester; Getulio Vargas Foundation; University System of Georgia; Georgia Institute of Technology
  摘要：This paper considers optimization problems where the objective is the sum of a function given by an expectation and a closed convex function, and proposes stochastic composite proximal bundle (SCPB) methods for solving it. Complexity guarantees are established for them without requiring knowledge of parameters associated with the problem instance. Moreover, it is shown that they have optimal complexity when these problem parameters are known. To the best of our knowledge, this is the first pro...
• A polynomial time algorithm for finding a minimum 4-partition of a submodular function AI翻译
  作者：Hirayama, Tsuyoshi; Liu, Yuhao; Makino, Kazuhisa; Shi, Ke; Xu, Chao
  作者单位：University of Electronic Science & Technology of China; Kyoto University
  摘要：In this paper, we study the minimum k-partition problem of submodular functions, i.e., given a finite set V and a submodular function f : 2(V) -> R, computing a k-partition {V-1, ... , V-k} of V with minimum Sigma k(i=1) f(V-i). The problem is a natural generalization of the minimum k-cut problem in graphs and hypergraphs. It is known that the problem is NP-hard for general k, and solvable in polynomial time for fixed k <= 3. In this paper, we construct the first polynomial-time algorithm for ...
• The limits of local search for weighted k-set packing AI翻译
  作者：Neuwohner, Meike
  作者单位：University of Bonn
  摘要：We consider the weighted k-set packing problem, where, given a collection S of sets, each of cardinality at most k, and a positive weight function w : S -> Q(>0), the task is to find a sub-collection of S consisting of pairwise disjoint sets of maximum total weight. As this problem does not permit a polynomial-time o( k/ log k )-approximation unless P = N P (Hazan et al. in Comput Complex 15:20-39, 2006. https://doi.org/ 10.1007/s00037-006-0205-6), most previous approaches rely on local search...
• Global stability of first-order methods for coercive tame functions AI翻译
  作者：Josz, Cedric; Lai, Lexiao
  作者单位：Columbia University
  摘要：We consider first-order methods with constant step size for minimizing locally Lipschitz coercive functions that are tame in an o-minimal structure on the real field. We prove that if the method is approximated by subgradient trajectories, then the iterates eventually remain in a neighborhood of a connected component of the set of critical points. Under suitable method-dependent regularity assumptions, this result applies to the subgradient method with momentum, the stochastic subgradient meth...
• Approximation algorithms for flexible graph connectivity AI翻译
  作者：Boyd, Sylvia; Cheriyan, Joseph; Haddadan, Arash; Ibrahimpur, Sharat
  作者单位：University of Ottawa; University of Waterloo; Amazon.com; University of London; London School Economics & Political Science
  摘要：We present approximation algorithms for several network design problems in the model of flexible graph connectivity (Adjiashvili et al., in: IPCO, pp 13-26, 2020, Math Program 1-33, 2021). Let k >== 1, p >= 1 and q >= 0 be integers. In an instance of the ( p, q)-Flexible Graph Connectivity problem, denoted ( p, q)-FGC, we have an undirected connected graph G = (V, E), a partition of E into a set of safe edges l and a set of unsafe edges U, and nonnegative costs c : E -> R(>=)0 on the edges. A ...
• Fair division of graphs and of tangled cakes AI翻译
  作者：Igarashi, Ayumi; Zwicker, William S.
  作者单位：Research Organization of Information & Systems (ROIS); National Institute of Informatics (NII) - Japan; Union College; Istanbul Bilgi University; CY Cergy Paris Universite
  摘要：Fair division has been studied in both continuous and discrete contexts. One strand of the continuous literature seeks to award each agent with a single connected piece-a subinterval. The analogue for the discrete case corresponds to the fair division of a graph, where allocations must be contiguous so that each bundle of vertices is required to induce a connected subgraph. With envy-freeness up to one item (EF1) as the fairness criterion, however, positive results for three or more agents hav...
• The core of a transferable utility game as the solution to a public good market demand problem AI翻译
  作者：Edelman, Paul H.; Van der Linden, Martin; Weymark, John A.
  作者单位：Vanderbilt University; Vanderbilt University; Emory University; Vanderbilt University
  摘要：The core of a monotonic transferable utility (TU) game is shown to be the set of prices that incentivize each individual to demand the grand coalition in a market demand problem in which the goods being demanded are coalitions viewed as excluable public goods. It is also shown that the core is the intersection of superdifferentials evaluated at the grand coalition of the covers of person-specific TU games derived from the original game. These characterizations of the core demonstrate how a mar...
• Machine learning augmented branch and bound for mixed integer linear programming AI翻译
  作者：Scavuzzo, Lara; Aardal, Karen; Lodi, Andrea; Yorke-Smith, Neil
  作者单位：Delft University of Technology; Technion Israel Institute of Technology
  摘要：Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. The main engine for solving MILPs is the branch-and-bound algorithm. Adding to the enormous algorithmic progress in MILP solving of the past decades, in more recent years there has been an explosive development in the use of machine learning for enhancing all main tasks involved in the branch-and-bound algorithm. These include primal heuris...
• The simultaneous semi-random model for TSP AI翻译
  作者：Balkanski, Eric; Faenza, Yuri; Kubik, Mathieu
  作者单位：Columbia University
  摘要：Worst-case analysis is a performance measure that is often too pessimistic to indicate which algorithms we should use in practice. A classical example is in the context of the Euclidean Traveling Salesman Problem (TSP) in the plane, where local search performs very well in practice even though it only achieves an O ((log log n)/ (log n) ) worst case approximation ratio. In such cases, a natural alternative approach to worst-case analysis is to analyze the performance of algorithms in semi-rand...
• Simple odd β-cycle inequalities for binary polynomial optimization AI翻译
  作者：Del Pia, Alberto; Walter, Matthias
  作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison; University of Twente
  摘要：We consider themultilinear polytope which arises naturally in binary polynomial optimization. Del Pia and Di Gregorio introduced the class of odd ss-cycle inequalities valid for this polytope, showed that these generally have Chvatal rank 2 with respect to the standard relaxation and that, together with flower inequalities, they yield a perfect formulation for cycle hypergraph instances. Moreover, they describe a separation algorithm in case the instance is a cycle hypergraph. We introduce a w...