发布求助
文献互助 智能选刊 最新文献

Mathematical Programming最新文献

筛选
英文 中文
Configuration balancing for stochastic requests 随机请求的配置平衡
IF 2.7 2区 数学
Mathematical Programming Pub Date : 2024-08-08 DOI: 10.1007/s10107-024-02132-w
Franziska Eberle, Anupam Gupta, Nicole Megow, Benjamin Moseley, Rudy Zhou
{"title":"Configuration balancing for stochastic requests","authors":"Franziska Eberle, Anupam Gupta, Nicole Megow, Benjamin Moseley, Rudy Zhou","doi":"10.1007/s10107-024-02132-w","DOIUrl":"https://doi.org/10.1007/s10107-024-02132-w","url":null,"abstract":"<p>The configuration balancing problem with stochastic requests generalizes well-studied resource allocation problems such as load balancing and virtual circuit routing. There are given <i>m</i> resources and <i>n</i> requests; each request has multiple possible <i>configurations</i>, each of which increases the load of each resource by some amount. The goal is to select one configuration for each request to minimize the <i>makespan</i>: the load of the most-loaded resource. In the stochastic setting, the amount by which a configuration increases the resource load is uncertain until the configuration is chosen, but we are given a probability distribution. We develop both offline and online algorithms for configuration balancing with stochastic requests. When the requests are known offline, we give a non-adaptive policy for configuration balancing with stochastic requests that <span>(O(frac{log m}{log log m}))</span>-approximates the optimal adaptive policy, which matches a known lower bound for the special case of load balancing on identical machines. When requests arrive online in a list, we give a non-adaptive policy that is <span>(O(log m))</span> competitive. Again, this result is asymptotically tight due to information-theoretic lower bounds for special cases (e.g., for load balancing on unrelated machines). Finally, we show how to leverage adaptivity in the special case of load balancing on <i>related</i> machines to obtain a constant-factor approximation offline and an <span>(O(log log m))</span>-approximation online. A crucial technical ingredient in all of our results is a new structural characterization of the optimal adaptive policy that allows us to limit the correlations between its decisions.\u0000</p>","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonsmooth convex–concave saddle point problems with cardinality penalties 有数量惩罚的非光滑凸凹鞍点问题
IF 2.7 2区 数学
Mathematical Programming Pub Date : 2024-08-08 DOI: 10.1007/s10107-024-02123-x
Wei Bian, Xiaojun Chen
{"title":"Nonsmooth convex–concave saddle point problems with cardinality penalties","authors":"Wei Bian, Xiaojun Chen","doi":"10.1007/s10107-024-02123-x","DOIUrl":"https://doi.org/10.1007/s10107-024-02123-x","url":null,"abstract":"<p>In this paper, we focus on a class of convexly constrained nonsmooth convex–concave saddle point problems with cardinality penalties. Although such nonsmooth nonconvex–nonconcave and discontinuous min–max problems may not have a saddle point, we show that they have a local saddle point and a global minimax point, and some local saddle points have the lower bound properties. We define a class of strong local saddle points based on the lower bound properties for stability of variable selection. Moreover, we give a framework to construct continuous relaxations of the discontinuous min–max problems based on convolution, such that they have the same saddle points with the original problem. We also establish the relations between the continuous relaxation problems and the original problems regarding local saddle points, global minimax points, local minimax points and stationary points. Finally, we illustrate our results with distributionally robust sparse convex regression, sparse robust bond portfolio construction and sparse convex–concave logistic regression saddle point problems.</p>","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimizing for strategy diversity in the design of video games 在设计电子游戏时优化策略多样性
IF 2.7 2区 数学
Mathematical Programming Pub Date : 2024-08-08 DOI: 10.1007/s10107-024-02126-8
Oussama Hanguir, Will Ma, Jiangze Han, Christopher Thomas Ryan
{"title":"Optimizing for strategy diversity in the design of video games","authors":"Oussama Hanguir, Will Ma, Jiangze Han, Christopher Thomas Ryan","doi":"10.1007/s10107-024-02126-8","DOIUrl":"https://doi.org/10.1007/s10107-024-02126-8","url":null,"abstract":"<p>We consider the problem of designing a linear program that has diverse solutions as the right-hand side varies. This problem arises in video game settings where designers aim to have players use different “weapons” or “tactics” as they progress. We model this design question as a choice over the constraint matrix <i>A</i> and cost vector <i>c</i> to maximize the number of possible <i>supports</i> of unique optimal solutions (what we call “loadouts”) of Linear Programs <span>(max {c^top x mid Ax le b, x ge 0})</span> with nonnegative data considered over all resource vectors <i>b</i>. We provide an upper bound on the optimal number of loadouts and provide a family of constructions that have an asymptotically optimal number of loadouts. The upper bound is based on a connection between our problem and the study of triangulations of point sets arising from polyhedral combinatorics, and specifically the combinatorics of the cyclic polytope. Our asymptotically optimal construction also draws inspiration from the properties of the cyclic polytope.</p>","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unified smoothing approach for best hyperparameter selection problem using a bilevel optimization strategy 使用双层优化策略解决最佳超参数选择问题的统一平滑法
IF 2.7 2区 数学
Mathematical Programming Pub Date : 2024-08-08 DOI: 10.1007/s10107-024-02113-z
Jan Harold Alcantara, Chieu Thanh Nguyen, Takayuki Okuno, Akiko Takeda, Jein-Shan Chen
{"title":"Unified smoothing approach for best hyperparameter selection problem using a bilevel optimization strategy","authors":"Jan Harold Alcantara, Chieu Thanh Nguyen, Takayuki Okuno, Akiko Takeda, Jein-Shan Chen","doi":"10.1007/s10107-024-02113-z","DOIUrl":"https://doi.org/10.1007/s10107-024-02113-z","url":null,"abstract":"<p>Strongly motivated from applications in various fields including machine learning, the methodology of sparse optimization has been developed intensively so far. Especially, the advancement of algorithms for solving problems with nonsmooth regularizers has been remarkable. However, those algorithms suppose that weight parameters of regularizers, called hyperparameters hereafter, are pre-fixed, but it is a crucial matter how the best hyperparameter should be selected. In this paper, we focus on the hyperparameter selection of regularizers related to the <span>(ell _p)</span> function with <span>(0&lt;ple 1)</span> and apply a bilevel programming strategy, wherein we need to solve a bilevel problem, whose lower-level problem is nonsmooth, possibly nonconvex and non-Lipschitz. Recently, for solving a bilevel problem for hyperparameter selection of the pure <span>(ell _p (0&lt;p le 1))</span> regularizer Okuno et al. discovered new necessary optimality conditions, called SB(scaled bilevel)-KKT conditions, and further proposed a smoothing-type algorithm using a specific smoothing function. However, this optimality measure is loose in the sense that there could be many points that satisfy the SB-KKT conditions. In this work, we propose new bilevel KKT conditions, which are new necessary optimality conditions tighter than the ones proposed by Okuno et al. Moreover, we propose a unified smoothing approach using smoothing functions that belong to the Chen-Mangasarian class, and then prove that generated iteration points accumulate at bilevel KKT points under milder constraint qualifications. Another contribution is that our approach and analysis are applicable to a wider class of regularizers. Numerical comparisons demonstrate which smoothing functions work well for hyperparameter optimization via bilevel optimization approach.</p>","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A radial basis function method for noisy global optimisation 噪声全局优化的径向基函数方法
IF 2.7 2区 数学
Mathematical Programming Pub Date : 2024-08-08 DOI: 10.1007/s10107-024-02125-9
Dirk Banholzer, Jörg Fliege, Ralf Werner
{"title":"A radial basis function method for noisy global optimisation","authors":"Dirk Banholzer, Jörg Fliege, Ralf Werner","doi":"10.1007/s10107-024-02125-9","DOIUrl":"https://doi.org/10.1007/s10107-024-02125-9","url":null,"abstract":"<p>We present a novel response surface method for global optimisation of an expensive and noisy (black-box) objective function, where error bounds on the deviation of the observed noisy function values from their true counterparts are available. The method is based on Gutmann’s well-established RBF method for minimising an expensive and deterministic objective function, which has become popular both from a theoretical and practical perspective. To construct suitable radial basis function approximants to the objective function and to determine new sample points for successive evaluation of the expensive noisy objective, the method uses a regularised least-squares criterion. In particular, new points are defined by means of a target value, analogous to the original RBF method. We provide essential convergence results, and provide a numerical illustration of the method by means of a simple test problem.\u0000</p>","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimizing distortion riskmetrics with distributional uncertainty 优化具有分布不确定性的扭曲风险度量
IF 2.7 2区 数学
Mathematical Programming Pub Date : 2024-07-29 DOI: 10.1007/s10107-024-02128-6
Silvana M. Pesenti, Qiuqi Wang, Ruodu Wang
{"title":"Optimizing distortion riskmetrics with distributional uncertainty","authors":"Silvana M. Pesenti, Qiuqi Wang, Ruodu Wang","doi":"10.1007/s10107-024-02128-6","DOIUrl":"https://doi.org/10.1007/s10107-024-02128-6","url":null,"abstract":"<p>Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not necessarily monotone or convex. One of our central findings is a unifying result that allows to convert an optimization of a non-convex distortion riskmetric with distributional uncertainty to a convex one induced from the concave envelope of the distortion function, leading to practical tractability. A sufficient condition to the unifying equivalence result is the novel notion of closedness under concentration, a variation of which is also shown to be necessary for the equivalence. Our results include many special cases that are well studied in the optimization literature, including but not limited to optimizing probabilities, Value-at-Risk, Expected Shortfall, Yaari’s dual utility, and differences between distortion risk measures, under various forms of distributional uncertainty. We illustrate our theoretical results via applications to portfolio optimization, optimization under moment constraints, and preference robust optimization.</p>","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141866962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence in distribution of randomized algorithms: the case of partially separable optimization 随机算法分布的收敛性：部分可分离优化的案例
IF 2.7 2区 数学
Mathematical Programming Pub Date : 2024-07-27 DOI: 10.1007/s10107-024-02124-w
D. Russell Luke
{"title":"Convergence in distribution of randomized algorithms: the case of partially separable optimization","authors":"D. Russell Luke","doi":"10.1007/s10107-024-02124-w","DOIUrl":"https://doi.org/10.1007/s10107-024-02124-w","url":null,"abstract":"<p>We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators and distributions behind the iterates of stochastic algorithms, and in particular the regularity of Markov operators and rates of convergence of the distributions of the corresponding Markov chains. This provides a detailed characterization of the moments of the sequences beyond just the expected behavior. This also serves as a case study of how randomization restores favorable properties to algorithms that iterations of only partial information destroys. We demonstrate this on stochastic blockwise implementations of the forward–backward and Douglas–Rachford algorithms for nonconvex (and, as a special case, convex), nonsmooth optimization.</p>","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On supervalid inequalities for binary interdiction games 论二元互斥博弈的监督不等式
IF 2.7 2区 数学
Mathematical Programming Pub Date : 2024-07-27 DOI: 10.1007/s10107-024-02111-1
Ningji Wei, Jose L. Walteros
{"title":"On supervalid inequalities for binary interdiction games","authors":"Ningji Wei, Jose L. Walteros","doi":"10.1007/s10107-024-02111-1","DOIUrl":"https://doi.org/10.1007/s10107-024-02111-1","url":null,"abstract":"<p>Supervalid inequalities are a specific type of constraints often used within the branch-and-cut framework to strengthen the linear relaxation of mixed-integer programs. These inequalities share the particular characteristic of potentially removing feasible integer solutions as long as they are already dominated by an incumbent solution. This paper focuses on supervalid inequalities for solving binary interdiction games. Specifically, we provide a general characterization of inequalities that are derived from bipartitions of the leader’s strategy set and develop an algorithmic approach to use them. This includes the design of two verification subroutines that we apply for separation purposes. We provide three general examples in which we apply our results to solve binary interdiction games targeting shortest paths, spanning trees, and vertex covers. Finally, we prove that the separation procedure is efficient for the class of interdiction games defined on greedoids—a type of set system that generalizes many others such as matroids and antimatroids.</p>","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The pseudo-Boolean polytope and polynomial-size extended formulations for binary polynomial optimization 二元多项式优化的伪布尔多面体和多项式大小扩展公式
IF 2.7 2区 数学
Mathematical Programming Pub Date : 2024-07-22 DOI: 10.1007/s10107-024-02122-y
Alberto Del Pia, Aida Khajavirad
{"title":"The pseudo-Boolean polytope and polynomial-size extended formulations for binary polynomial optimization","authors":"Alberto Del Pia, Aida Khajavirad","doi":"10.1007/s10107-024-02122-y","DOIUrl":"https://doi.org/10.1007/s10107-024-02122-y","url":null,"abstract":"<p>With the goal of obtaining strong relaxations for binary polynomial optimization problems, we introduce the pseudo-Boolean polytope defined as the set of binary points <span>(z in {0,1}^{V cup S})</span> satisfying a collection of equalities of the form <span>(z_s = prod _{v in s} sigma _s(z_v))</span>, for all <span>(s in S)</span>, where <span>(sigma _s(z_v) in {z_v, 1-z_v})</span>, and where <i>S</i> is a multiset of subsets of <i>V</i>. By representing the pseudo-Boolean polytope via a signed hypergraph, we obtain sufficient conditions under which this polytope has a polynomial-size extended formulation. Our new framework unifies and extends all prior results on the existence of polynomial-size extended formulations for the convex hull of the feasible region of binary polynomial optimization problems of degree at least three.</p>","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A trust region-type normal map-based semismooth Newton method for nonsmooth nonconvex composite optimization 基于信任区域型法线图的非平滑非凸复合优化半平滑牛顿法
IF 2.7 2区 数学
Mathematical Programming Pub Date : 2024-07-22 DOI: 10.1007/s10107-024-02110-2
Wenqing Ouyang, Andre Milzarek
{"title":"A trust region-type normal map-based semismooth Newton method for nonsmooth nonconvex composite optimization","authors":"Wenqing Ouyang, Andre Milzarek","doi":"10.1007/s10107-024-02110-2","DOIUrl":"https://doi.org/10.1007/s10107-024-02110-2","url":null,"abstract":"<p>We propose a novel trust region method for solving a class of nonsmooth, nonconvex composite-type optimization problems. The approach embeds inexact semismooth Newton steps for finding zeros of a normal map-based stationarity measure for the problem in a trust region framework. Based on a new merit function and acceptance mechanism, global convergence and transition to fast local q-superlinear convergence are established under standard conditions. In addition, we verify that the proposed trust region globalization is compatible with the Kurdyka–Łojasiewicz inequality yielding finer convergence results. Experiments on sparse logistic regression, image compression, and a constrained log-determinant problem illustrate the efficiency of the proposed algorithm.</p>","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信