SIAM Journal on Optimization最新文献_第9页

A Path-Based Approach to Constrained Sparse Optimization 基于路径的约束稀疏优化方法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-21 DOI: 10.1137/22m1535498

Nadav Hallak

引用次数: 0

Accelerating Primal-Dual Methods for Regularized Markov Decision Processes 加速正则化马尔可夫决策过程的原始-双重方法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-20 DOI: 10.1137/21m1468851

Haoya Li, Hsiang-Fu Yu, Lexing Ying, Inderjit S. Dhillon

引用次数: 0

Safe and Verified Gomory Mixed-Integer Cuts in a Rational Mixed-Integer Program Framework 合理混合整数程序框架中安全且经过验证的高莫里混合整数切割

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-16 DOI: 10.1137/23m156046x

Leon Eifler, Ambros Gleixner

{"title":"Safe and Verified Gomory Mixed-Integer Cuts in a Rational Mixed-Integer Program Framework","authors":"Leon Eifler, Ambros Gleixner","doi":"10.1137/23m156046x","DOIUrl":"https://doi.org/10.1137/23m156046x","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 1, Page 742-763, March 2024. <br/> Abstract. This paper is concerned with the exact solution of mixed-integer programs (MIPs) over the rational numbers, i.e., without any roundoff errors and error tolerances. Here, one computational bottleneck that should be avoided whenever possible is to employ large-scale symbolic computations. Instead it is often possible to use safe directed rounding methods, e.g., to generate provably correct dual bounds. In this work, we continue to leverage this paradigm and extend an exact branch-and-bound framework by separation routines for safe cutting planes, based on the approach first introduced by Cook, Dash, Fukasawa, and Goycoolea in 2009 [INFORMS J. Comput., 21 (2009), pp. 641–649]. Constraints are aggregated safely using approximate dual multipliers from an LP solve, followed by mixed-integer rounding to generate provably valid, although slightly weaker inequalities. We generalize this approach to problem data that is not representable in floating-point arithmetic, add routines for controlling the encoding length of the resulting cutting planes, and show how these cutting planes can be verified according to the VIPR certificate standard. Furthermore, we analyze the performance impact of these cutting planes in the context of an exact MIP framework, showing that we can solve 21.5% more instances to exact optimality and reduce solving times by 26.8% on the MIPLIB 2017 benchmark test set.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"35 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Linear Programming on the Stiefel Manifold Stiefel Manifold 上的线性规划

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-15 DOI: 10.1137/23m1552243

Mengmeng Song, Yong Xia

引用次数: 0

Bounds for Multistage Mixed-Integer Distributionally Robust Optimization 多阶段混合整数分布式稳健优化的界限

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-13 DOI: 10.1137/22m147178x

Güzin Bayraksan, Francesca Maggioni, Daniel Faccini, Ming Yang

{"title":"Bounds for Multistage Mixed-Integer Distributionally Robust Optimization","authors":"Güzin Bayraksan, Francesca Maggioni, Daniel Faccini, Ming Yang","doi":"10.1137/22m147178x","DOIUrl":"https://doi.org/10.1137/22m147178x","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 1, Page 682-717, March 2024. <br/> Abstract. Multistage mixed-integer distributionally robust optimization (DRO) forms a class of extremely challenging problems since their size grows exponentially with the number of stages. One way to model the uncertainty in multistage DRO is by creating sets of conditional distributions (the so-called conditional ambiguity sets) on a finite scenario tree and requiring that such distributions remain close to nominal conditional distributions according to some measure of similarity/distance (e.g., [math]-divergences or Wasserstein distance). In this paper, new bounding criteria for this class of difficult decision problems are provided through scenario grouping using the ambiguity sets associated with various commonly used [math]-divergences and the Wasserstein distance. Our approach does not require any special problem structure such as linearity, convexity, stagewise independence, and so forth. Therefore, while we focus on multistage mixed-integer DRO, our bounds can be applied to a wide range of DRO problems including two-stage and multistage, with or without integer variables, convex or nonconvex, and nested or nonnested formulations. Numerical results on a multistage mixed-integer production problem show the efficiency of the proposed approach through different choices of partition strategies, ambiguity sets, and levels of robustness.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"18 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 Riemannian Proximal Newton Method 黎曼近端牛顿法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-09 DOI: 10.1137/23m1565097

Wutao Si, P.-A. Absil, Wen Huang, Rujun Jiang, Simon Vary

引用次数: 0

Various Notions of Nonexpansiveness Coincide for Proximal Mappings of Functions 函数近端映射的各种非扩张性概念相吻合

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-09 DOI: 10.1137/23m1597009

Honglin Luo, Xianfu Wang, Xinmin Yang

引用次数: 0

Second Order Conditions to Decompose Smooth Functions as Sums of Squares 将平稳函数分解为平方和的二阶条件

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-08 DOI: 10.1137/22m1480914

Ulysse Marteau-Ferey, Francis Bach, Alessandro Rudi

{"title":"Second Order Conditions to Decompose Smooth Functions as Sums of Squares","authors":"Ulysse Marteau-Ferey, Francis Bach, Alessandro Rudi","doi":"10.1137/22m1480914","DOIUrl":"https://doi.org/10.1137/22m1480914","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 1, Page 616-641, March 2024. <br/> Abstract. We consider the problem of decomposing a regular nonnegative function as a sum of squares of functions which preserve some form of regularity. In the same way as decomposing nonnegative polynomials as sum of squares of polynomials allows one to derive methods in order to solve global optimization problems on polynomials, decomposing a regular function as a sum of squares allows one to derive methods to solve global optimization problems on more general functions. As the regularity of the functions in the sum of squares decomposition is a key indicator in analyzing the convergence and speed of convergence of optimization methods, it is important to have theoretical results guaranteeing such a regularity. In this work, we show second order sufficient conditions in order for a [math] times continuously differentiable nonnegative function to be a sum of squares of [math] differentiable functions. The main hypothesis is that, locally, the function grows quadratically in directions which are orthogonal to its set of zeros. The novelty of this result, compared to previous works is that it allows sets of zeros which are continuous as opposed to discrete, and also applies to manifolds as opposed to open sets of [math]. This has applications in problems where manifolds of minimizers or zeros typically appear, such as in optimal transport, and for minimizing functions defined on manifolds.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"18 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Harmonic Hierarchies for Polynomial Optimization 用于多项式优化的谐波层次结构

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-06 DOI: 10.1137/22m1484511

Sergio Cristancho, Mauricio Velasco

引用次数: 0

Convergence Rate Analysis of a Dykstra-Type Projection Algorithm Dykstra 型投影算法的收敛率分析

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-06 DOI: 10.1137/23m1545781

Xiaozhou Wang, Ting Kei Pong

{"title":"Convergence Rate Analysis of a Dykstra-Type Projection Algorithm","authors":"Xiaozhou Wang, Ting Kei Pong","doi":"10.1137/23m1545781","DOIUrl":"https://doi.org/10.1137/23m1545781","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 1, Page 563-589, March 2024. <br/> Abstract. Given closed convex sets [math], [math], and some nonzero linear maps [math], [math], of suitable dimensions, the multiset split feasibility problem aims at finding a point in [math] based on computing projections onto [math] and multiplications by [math] and [math]. In this paper, we consider the associated best approximation problem, i.e., the problem of computing projections onto [math]; we refer to this problem as the best approximation problem in multiset split feasibility settings (BA-MSF). We adapt the Dykstra’s projection algorithm, which is classical for solving the BA-MSF in the special case when all [math], to solve the general BA-MSF. Our Dykstra-type projection algorithm is derived by applying (proximal) coordinate gradient descent to the Lagrange dual problem, and it only requires computing projections onto [math] and multiplications by [math] and [math] in each iteration. Under a standard relative interior condition and a genericity assumption on the point we need to project, we show that the dual objective satisfies the Kurdyka-Łojasiewicz property with an explicitly computable exponent on a neighborhood of the (typically unbounded) dual solution set when each [math] is [math]-cone reducible for some [math]: this class of sets covers the class of [math]-cone reducible sets, which include all polyhedrons, second-order cone, and the cone of positive semidefinite matrices as special cases. Using this, explicit convergence rate (linear or sublinear) of the sequence generated by the Dykstra-type projection algorithm is derived. Concrete examples are constructed to illustrate the necessity of some of our assumptions.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"1 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139773221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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