Mathematical Programming最新文献_第3页

Competitive kill-and-restart and preemptive strategies for non-clairvoyant scheduling 非千里眼调度的竞争性杀死-重启和抢先策略

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-07-22 DOI: 10.1007/s10107-024-02118-8

Sven Jäger, Guillaume Sagnol, Daniel Schmidt genannt Waldschmidt, Philipp Warode

{"title":"Competitive kill-and-restart and preemptive strategies for non-clairvoyant scheduling","authors":"Sven Jäger, Guillaume Sagnol, Daniel Schmidt genannt Waldschmidt, Philipp Warode","doi":"10.1007/s10107-024-02118-8","DOIUrl":"https://doi.org/10.1007/s10107-024-02118-8","url":null,"abstract":"We study kill-and-restart and preemptive strategies for the fundamental scheduling problem of minimizing the sum of weighted completion times on a single machine in the non-clairvoyant setting. First, we show a lower bound of 3 for any deterministic non-clairvoyant kill-and-restart strategy. Then, we give for any (b > 1) a tight analysis for the natural b-scaling kill-and-restart strategy as well as for a randomized variant of it. In particular, we show a competitive ratio of ((1+3sqrt{3})approx 6.197) for the deterministic and of (approx 3.032) for the randomized strategy, by making use of the largest eigenvalue of a Toeplitz matrix. In addition, we show that the preemptive Weighted Shortest Elapsed Time First (WSETF) rule is 2-competitive when jobs are released online, matching the lower bound for the unit weight case with trivial release dates for any non-clairvoyant algorithm. Using this result as well as the competitiveness of round-robin for multiple machines, we prove performance guarantees smaller than 10 for adaptions of the b-scaling strategy to online release dates and unweighted jobs on identical parallel machines.","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":"141746019","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 the geometry and refined rate of primal–dual hybrid gradient for linear programming 论线性规划的初等-双重混合梯度的几何形状和精炼率

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-07-17 DOI: 10.1007/s10107-024-02109-9

Haihao Lu, Jinwen Yang

{"title":"On the geometry and refined rate of primal–dual hybrid gradient for linear programming","authors":"Haihao Lu, Jinwen Yang","doi":"10.1007/s10107-024-02109-9","DOIUrl":"https://doi.org/10.1007/s10107-024-02109-9","url":null,"abstract":"We study the convergence behaviors of primal–dual hybrid gradient (PDHG) for solving linear programming (LP). PDHG is the base algorithm of a new general-purpose first-order method LP solver, PDLP, which aims to scale up LP by taking advantage of modern computing architectures. Despite its numerical success, the theoretical understanding of PDHG for LP is still very limited; the previous complexity result relies on the global Hoffman constant of the KKT system, which is known to be very loose and uninformative. In this work, we aim to develop a fundamental understanding of the convergence behaviors of PDHG for LP and to develop a refined complexity rate that does not rely on the global Hoffman constant. We show that there are two major stages of PDHG for LP: in Stage I, PDHG identifies active variables and the length of the first stage is driven by a certain quantity which measures how close the non-degeneracy part of the LP instance is to degeneracy; in Stage II, PDHG effectively solves a homogeneous linear inequality system, and the complexity of the second stage is driven by a well-behaved local sharpness constant of the system. This finding is closely related to the concept of partial smoothness in non-smooth optimization, and it is the first complexity result of finite time identification without the non-degeneracy assumption. An interesting implication of our results is that degeneracy itself does not slow down the convergence of PDHG for LP, but near-degeneracy does.","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717803","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

Distributional utility preference robust optimization models in multi-attribute decision making 多属性决策中的分配效用偏好稳健优化模型

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-07-17 DOI: 10.1007/s10107-024-02114-y

Jian Hu, Dali Zhang, Huifu Xu, Sainan Zhang

{"title":"Distributional utility preference robust optimization models in multi-attribute decision making","authors":"Jian Hu, Dali Zhang, Huifu Xu, Sainan Zhang","doi":"10.1007/s10107-024-02114-y","DOIUrl":"https://doi.org/10.1007/s10107-024-02114-y","url":null,"abstract":"Utility preference robust optimization (PRO) has recently been proposed to deal with optimal decision-making problems where the decision maker’s (DM’s) preference over gains and losses is ambiguous. In this paper, we take a step further to investigate the case that the DM’s preference is random. We propose to use a random utility function to describe the DM’s preference and develop distributional utility preference robust optimization (DUPRO) models when the distribution of the random utility function is ambiguous. We concentrate on data-driven problems where samples of the random parameters are obtainable but the sample size may be relatively small. In the case when the random utility functions are of piecewise linear structure, we propose a bootstrap method to construct the ambiguity set and demonstrate how the resulting DUPRO can be solved by a mixed-integer linear program. The piecewise linear structure is versatile in its ability to incorporate classical non-parametric utility assessment methods into the sample generation of a random utility function. Next, we expand the proposed DUPRO models and computational schemes to address general cases where the random utility functions are not necessarily piecewise linear. We show how the DUPRO models with piecewise linear random utility functions can serve as approximations for the DUPRO models with general random utility functions and allow us to quantify the approximation errors. Finally, we carry out some performance studies of the proposed bootstrap-based DUPRO model and report the preliminary numerical test results. This paper is the first attempt to use distributionally robust optimization methods for PRO problems.\u0000","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717805","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

New notions of simultaneous diagonalizability of quadratic forms with applications to QCQPs 二次型同时对角化的新概念及其在 QCQPs 中的应用

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-07-17 DOI: 10.1007/s10107-024-02120-0

Alex L. Wang, Rujun Jiang

{"title":"New notions of simultaneous diagonalizability of quadratic forms with applications to QCQPs","authors":"Alex L. Wang, Rujun Jiang","doi":"10.1007/s10107-024-02120-0","DOIUrl":"https://doi.org/10.1007/s10107-024-02120-0","url":null,"abstract":"A set of quadratic forms is simultaneously diagonalizable via congruence (SDC) if there exists a basis under which each of the quadratic forms is diagonal. This property appears naturally when analyzing quadratically constrained quadratic programs (QCQPs) and has important implications in globally solving such problems using branch-and-bound methods. This paper extends the reach of the SDC property by studying two new weaker notions of simultaneous diagonalizability. Specifically, we say that a set of quadratic forms is almost SDC (ASDC) if it is the limit of SDC sets and d-restricted SDC (d-RSDC) if it is the restriction of an SDC set in up to d-many additional dimensions. In the context of QCQPs, these properties correspond to problems that may be diagonalized after arbitrarily small perturbations or after the introduction of d additional variables. Our main contributions are complete characterizations of the ASDC pairs and nonsingular triples of symmetric matrices, as well as a sufficient condition for the 1-RSDC property for pairs of symmetric matrices. Surprisingly, we show that every singular symmetric pair is ASDC and that almost every symmetric pair is 1-RSDC. We accompany our theoretical results with preliminary numerical experiments applying these constructions to solve QCQPs within branch-and-bound schemes.","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717804","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

Efficient separation of RLT cuts for implicit and explicit bilinear terms 隐式和显式双线性项的 RLT 切分的高效分离

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-07-16 DOI: 10.1007/s10107-024-02104-0

Ksenia Bestuzheva, Ambros Gleixner, Tobias Achterberg

{"title":"Efficient separation of RLT cuts for implicit and explicit bilinear terms","authors":"Ksenia Bestuzheva, Ambros Gleixner, Tobias Achterberg","doi":"10.1007/s10107-024-02104-0","DOIUrl":"https://doi.org/10.1007/s10107-024-02104-0","url":null,"abstract":"The reformulation–linearization technique (RLT) is a prominent approach to constructing tight linear relaxations of non-convex continuous and mixed-integer optimization problems. The goal of this paper is to extend the applicability and improve the performance of RLT for bilinear product relations. First, we present a method for detecting bilinear product relations implicitly contained in mixed-integer linear programs, which is based on analyzing linear constraints with binary variables, thus enabling the application of bilinear RLT to a new class of problems. Strategies for filtering product relations are discussed and tested. Our second contribution addresses the high computational cost of RLT cut separation, which presents one of the major difficulties in applying RLT efficiently in practice. We propose a new RLT cutting plane separation algorithm which identifies combinations of linear constraints and bound factors that are expected to yield an inequality that is violated by the current relaxation solution. This algorithm is applicable to RLT cuts generated for all types of bilinear terms, including but not limited to the detected implicit products. A detailed computational study based on independent implementations in two solvers evaluates the performance impact of the proposed methods.","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141722007","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

Structural iterative rounding for generalized k-median problems 广义 K 中值问题的结构性迭代舍入

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-07-10 DOI: 10.1007/s10107-024-02119-7

Anupam Gupta, Benjamin Moseley, Rudy Zhou

{"title":"Structural iterative rounding for generalized k-median problems","authors":"Anupam Gupta, Benjamin Moseley, Rudy Zhou","doi":"10.1007/s10107-024-02119-7","DOIUrl":"https://doi.org/10.1007/s10107-024-02119-7","url":null,"abstract":"This paper considers approximation algorithms for generalized k-median problems. These problems can be informally described as k-median with a constant number of extra constraints, and includes k-median with outliers, and knapsack median. Our first contribution is a pseudo-approximation algorithm for generalized k-median that outputs a 6.387-approximate solution, with a constant number of fractional variables. The algorithm builds on the iterative rounding framework introduced by Krishnaswamy, Li, and Sandeep for k-median with outliers as reported (Krishnaswamy et al. in: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018). The main technical innovation is allowing richer constraint sets in the iterative rounding and using the structure of the resulting extreme points. Using our pseudo-approximation algorithm, we give improved approximation algorithms for k-median with outliers and knapsack median. This involves combining our pseudo-approximation with pre- and post-processing steps to round a constant number of fractional variables at a small increase in cost. Our algorithms achieve approximation ratios (6.994 + epsilon ) and (6.387 + epsilon ) for k-median with outliers and knapsack median, respectively. These improve on the best-known approximation ratio (7.081 + epsilon ) for both problems as reported (Krishnaswamy et al. in: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018).","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567652","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

Monoidal strengthening and unique lifting in MIQCPs MIQCP 中的单值加强和唯一提升

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-07-08 DOI: 10.1007/s10107-024-02112-0

Antonia Chmiela, Gonzalo Muñoz, Felipe Serrano

引用次数: 0

On circuit diameter bounds via circuit imbalances 通过电路失衡论电路直径边界

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-07-08 DOI: 10.1007/s10107-024-02107-x

Daniel Dadush, Zhuan Khye Koh, Bento Natura, László A. Végh

引用次数: 0

Optimal methods for convex nested stochastic composite optimization 凸嵌套随机复合优化的最优方法

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-07-05 DOI: 10.1007/s10107-024-02090-3

Zhe Zhang, Guanghui Lan

{"title":"Optimal methods for convex nested stochastic composite optimization","authors":"Zhe Zhang, Guanghui Lan","doi":"10.1007/s10107-024-02090-3","DOIUrl":"https://doi.org/10.1007/s10107-024-02090-3","url":null,"abstract":"Recently, convex nested stochastic composite optimization (NSCO) has received considerable interest for its applications in reinforcement learning and risk-averse optimization. However, existing NSCO algorithms have worse stochastic oracle complexities, by orders of magnitude, than those for simpler stochastic optimization problems without nested structures. Additionally, these algorithms require all outer-layer functions to be smooth, a condition violated by some important applications. This raises a question regarding whether the nested composition make stochastic optimization more difficult in terms of oracle complexity. In this paper, we answer the question by developing order-optimal algorithms for convex NSCO problems constructed from an arbitrary composition of smooth, structured non-smooth, and general non-smooth layer functions. When all outer-layer functions are smooth, we propose a stochastic sequential dual (SSD) method to achieve an oracle complexity of (mathcal {O}(1/epsilon ^2)) (resp., (mathcal {O}(1/epsilon ))) when the problem is convex (resp., strongly convex). If any outer-layer function is non-smooth, we propose a non-smooth stochastic sequential dual (nSSD) method to achieve an (mathcal {O}(1/epsilon ^2)) oracle complexity. We provide a lower complexity bound to show the latter (mathcal {O}(1/epsilon ^2)) complexity to be unimprovable, even under a strongly convex setting. All these complexity results seem to be new in the literature, and they indicate that convex NSCO problems have the same order of oracle complexity as problems without nested composition, except in the strongly convex and outer non-smooth cases.","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547945","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 the directional asymptotic approach in optimization theory 论优化理论中的定向渐近方法

IF 2.7 2区数学

Mathematical Programming Pub Date : 2024-07-05 DOI: 10.1007/s10107-024-02089-w

Matúš Benko, Patrick Mehlitz

{"title":"On the directional asymptotic approach in optimization theory","authors":"Matúš Benko, Patrick Mehlitz","doi":"10.1007/s10107-024-02089-w","DOIUrl":"https://doi.org/10.1007/s10107-024-02089-w","url":null,"abstract":"As a starting point of our research, we show that, for a fixed order (gamma ge 1), each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order 1), satisfies stationarity conditions in terms of a coderivative construction of order (gamma ), or is asymptotically stationary with respect to a critical direction as well as order (gamma ) in a certain sense. By ruling out the latter case with a constraint qualification not stronger than directional metric subregularity, we end up with new necessary optimality conditions comprising a mixture of limiting variational tools of orders 1 and (gamma ). These abstract findings are carved out for the broad class of geometric constraints and (gamma :=2), and visualized by examples from complementarity-constrained and nonlinear semidefinite optimization. As a byproduct of the particular setting (gamma :=1), our general approach yields new so-called directional asymptotic regularity conditions which serve as constraint qualifications guaranteeing M-stationarity of local minimizers. We compare these new regularity conditions with standard constraint qualifications from nonsmooth optimization. Further, we extend directional concepts of pseudo- and quasi-normality to arbitrary set-valued mappings. It is shown that these properties provide sufficient conditions for the validity of directional asymptotic regularity. Finally, a novel coderivative-like variational tool is used to construct sufficient conditions for the presence of directional asymptotic regularity. For geometric constraints, it is illustrated that all appearing objects can be calculated in terms of initial problem data.","PeriodicalId":18297,"journal":{"name":"Mathematical Programming","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547944","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