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Local Approximability of Max-Min and Min-Max Linear Programs

Patrik Floréen, Marja Hassinen, Joel Kaasinen, Petteri Kaski, Topi Musto, Jukka Suomela
2010 Theory of Computing Systems  
We study the approximability of max-min LPs and min-max LPs in a distributed setting; in particular, we focus on local algorithms (constant-time distributed algorithms).  ...  In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0. In a min-max LP, the objective is to minimise ρ subject to Ax ≤ ρ1, Cx ≥ 1, and x ≥ 0.  ...  This research was supported in part by the Academy of Finland, Grants 116547 and 117499, by Helsinki Graduate School in Computer Science and Engineering (Hecse), and by the Foundation of Nokia Corporation  ... 
doi:10.1007/s00224-010-9303-6 fatcat:xeaytjft5vbited3bwyfdyrtpu

An optimal local approximation algorithm for max-min linear programs

Patrik Floréen, Joel Kaasinen, Petteri Kaski, Jukka Suomela
2009 Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures - SPAA '09  
We present a local algorithm (constant-time distributed algorithm) for approximating max-min LPs.  ...  The approximation ratio of our algorithm is the best possible for any local algorithm; there is a matching unconditional lower bound.  ...  INTRODUCTION In a max-min linear program (max-min LP), the objective is to maximise min k∈K c k x subject to Ax ≤ 1, x ≥ 0 (1) or, equivalently, to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, x ≥ 0.  ... 
doi:10.1145/1583991.1584058 dblp:conf/spaa/FloreenKKS09 fatcat:ig3jhppizfezfb6vyavsvg2quq

Tight Local Approximation Results for Max-Min Linear Programs [chapter]

Patrik Floréen, Marja Hassinen, Petteri Kaski, Jukka Suomela
2008 Lecture Notes in Computer Science  
In a bipartite max-min LP, we are given a bipartite graph = (V ∪ I ∪ K, E), where each agent v ∈ V is adjacent to exactly one constraint i ∈ I and exactly one objective k ∈ K.  ...  As a methodological contribution, we introduce the technique of graph unfolding for the design of local approximation algorithms.  ...  , r ) = agents in radius r neighbourhood of v There is a local algorithm for max-min LPs with approximation ratio 1 + 2δ + o(δ) Theorem There is no local algorithm for max-min LPs with approximation  ... 
doi:10.1007/978-3-540-92862-1_2 fatcat:qsa2v6niujf6baftfbcczbbruu

Models and Algorithms for Optimal Piecewise-Linear Function Approximation

Eduardo Camponogara, Luiz Fernando Nazari
2015 Mathematical Problems in Engineering  
This paper presents a range of piecewise-linear models and algorithms to aid engineers to find an approximation that fits best their applications.  ...  The models include piecewise-linear functions with a fixed and maximum number of linear segments, lower and upper envelopes, strategies to ensure continuity, and a generalization of these models for stochastic  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2015/876862 fatcat:mg6yxlaapbcdrlm74ycgnzxuqi

Linearly constrained global optimization via piecewise-linear approximation

Hao Zhang, Shuning Wang
2008 Journal of Computational and Applied Mathematics  
solution by solving a set of standard linear programs.  ...  This paper considers the problem of optimizing a continuous nonlinear objective function subject to linear constraints via a piecewise-linear approximation.  ...  Step 4: ChooseS from S, then get the CPWL approximation (x) = min s∈S max j ∈s ( j , x) for f on D. Step 5: Obtain an optimal solution z * (s) and x * (s) of the linear program (27) for each s ∈S.  ... 
doi:10.1016/j.cam.2007.02.006 fatcat:5n2f2oawhbaehd3np72efwsvmy

Approximate separation of quantum gates and separation experiments of CNOT based on Particle Swarm Optimization algorithm [article]

Kan He, Shusen Liu, Jinchuan Hou
2022 arXiv   pre-print
We propose and study a problem involving the approximate separation of multipartite gates based on quantum-gate fidelity.  ...  For given multipartite and local gates, we conclude that the smaller is the maximal distance between the products of an arbitrary pair of eigenvalues, the greater is their gate fidelity.  ...  This work is partly supported by National Natural Science Foundation of China No. 11771011, 12071336. Correspondence should be addressed to K. He(hekanquantum@163.com).  ... 
arXiv:2201.05786v1 fatcat:wkz74fn7pbh4jmdx7rkcpzlray

Design of balanced MBA student teams

J Desrosiers, N Mladenović, D Villeneuve
2005 Journal of the Operational Research Society  
The min-max DBT problem min{max,—,;__7¢,),}. has a similar integer programming formulation.  ...  Two different ways of measuring the balance among teams are proposed: min-sum and min-max models.  ... 
doi:10.1057/palgrave.jors.2601775 fatcat:6ltspgsqsnggdcgheq6ytpmyn4

A quadratic programming approach to path smoothing

Yiming Zhao, Panagiotis Tsiotras
2011 Proceedings of the 2011 American Control Conference  
Some characteristic nodes of the path are updated in each iteration by solving a quadratic program, which is formulated based on the smoothness constraints and the local environment information.  ...  The proposed method is easy to implement and computationally efficient. Y. Zhao is a Ph.D. candidate with the  ...  Let K max = [K max,1 , K max,2 , . . . , K max,N ] T and K min = [K min,1 , K min,2 , . . . , K min,N ] T .  ... 
doi:10.1109/acc.2011.5990880 fatcat:rze2pxhpfjcttcwyv4n4yezwcq

Buffer overrun detection using linear programming and static analysis

Vinod Ganapathy, Somesh Jha, David Chandler, David Melski, David Vitek
2003 Proceedings of the 10th ACM conference on Computer and communication security - CCS '03  
We also present fast, scalable solvers based on linear programming, and demonstrate techniques to make the program analysis context sensitive.  ...  We demonstrate a light-weight analysis based on modeling C string manipulations as a linear program.  ...  We would like to thank the members of the Wisconsin Safety Analyzer research group, Michael Ferris, Aditya Rao and the anonymous reviewers for their suggestions.  ... 
doi:10.1145/948109.948155 dblp:conf/ccs/GanapathyJCMV03 fatcat:3e723oqg7vdsfeunmzazkwov5y

Buffer overrun detection using linear programming and static analysis

Vinod Ganapathy, Somesh Jha, David Chandler, David Melski, David Vitek
2003 Proceedings of the 10th ACM conference on Computer and communication security - CCS '03  
We also present fast, scalable solvers based on linear programming, and demonstrate techniques to make the program analysis context sensitive.  ...  We demonstrate a light-weight analysis based on modeling C string manipulations as a linear program.  ...  We would like to thank the members of the Wisconsin Safety Analyzer research group, Michael Ferris, Aditya Rao and the anonymous reviewers for their suggestions.  ... 
doi:10.1145/948152.948155 fatcat:jqnz4txfpjb2dchiertyujplwi

On Estimation Algorithms vs Approximation Algorithms

Uriel Feige, Marc Herbstritt
2008 Foundations of Software Technology and Theoretical Computer Science  
These algorithms run in polynomial time, and their performance is measured by their approximation ratio: the worst case ratio between the value of the solution produced and the value of the (unknown) optimal  ...  A way of coping with NP-hardness is by considering approximation algorithms.  ...  Hence the value of the linear program provides a constant factor estimation for the restricted assignment version of the max-min allocation problem.  ... 
doi:10.4230/lipics.fsttcs.2008.1767 dblp:conf/fsttcs/Feige08 fatcat:ukvanc6yond5jhbmthmgld2gia

Linear regression over the max-plus semiring: algorithms and applications [article]

James Hook
2017 arXiv   pre-print
Namely inferring a max-plus linear dynamical systems model from a noisy time series recording, inferring the edge lengths of a network from shortest path information and fitting a max-plus polynomial function  ...  In this paper we present theory, algorithms and applications for regression over the max- plus semiring.  ...  We also thank Henning Makholm for answering a question on Math Stack Exchange, which helped in the formulation of Theorem 6.2.  ... 
arXiv:1712.03499v1 fatcat:7fotyjlrf5ho7d6w3ml5warrzy

Page 3086 of Mathematical Reviews Vol. , Issue 90E [page]

1990 Mathematical Reviews  
Max-min problems with a pseudofractional objective function and generalized linear constraints are reduced to generalized bilinear max-min problems with linear constraints which can be solved by generalized  ...  The generalized linear fractional program is the problem T a; x+aj max t :Cx< x20}. sup max { ot an *e The authors use a different approach involving linear programming duality to obtain the (known) dual  ... 

EXPLICIT MIN-MAX MODEL PREDICTIVE CONTROL OF CONSTRAINED NONLINEAR SYSTEMS WITH MODEL UNCERTAINTY

Alexandra Grancharova, Tor A. Johansen
2005 IFAC Proceedings Volumes  
The explicit MPC controller is based on an orthogonal search tree structure of the state space partition and is designed by solving a min-max optimization problem.  ...  This paper presents an approximate multi-parametric nonlinear programming approach to explicit solution of constrained nonlinear model predictive control (MPC) problems in the presence of model uncertainty  ...  of the explicit min-max MPC and the state trajectories corresponding to Control State  ... 
doi:10.3182/20050703-6-cz-1902.00826 fatcat:2mitsffdenaujbzpjads5bzmxq

AReN: Assured ReLU NN Architecture for Model Predictive Control of LTI Systems [article]

James Ferlez, Yasser Shoukry
2019 arXiv   pre-print
Second, we show that we can efficiently over-approximate the number of affine regions in the optimal MPC controller without solving the MPC problem exactly.  ...  While several previous works were inspired by the fact that both ReLU NN controllers and optimal MPC controller are both Continuous, Piecewise-Linear (CPWL) functions, exploiting this similarity to design  ...  A natural means to approximate to the number of local linear functions of µ MPC is to approximate the number of maximal linear regions in µ MPC . Definition 3 (Linear Region of µ MPC ).  ... 
arXiv:1911.01608v1 fatcat:b3vzfghkdjgu5hzyif2ez473lu
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