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

2010
*
Theory of Computing Systems
*

We study the

doi:10.1007/s00224-010-9303-6
fatcat:xeaytjft5vbited3bwyfdyrtpu
*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 ...##
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An optimal local approximation algorithm for max-min linear programs

2009
*
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures - SPAA '09
*

We present a

doi:10.1145/1583991.1584058
dblp:conf/spaa/FloreenKKS09
fatcat:ig3jhppizfezfb6vyavsvg2quq
*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. ...##
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Tight Local Approximation Results for Max-Min Linear Programs
[chapter]

2008
*
Lecture Notes in Computer Science
*

In a bipartite

doi:10.1007/978-3-540-92862-1_2
fatcat:qsa2v6niujf6baftfbcczbbruu
*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*...##
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Models and Algorithms for Optimal Piecewise-Linear Function Approximation

2015
*
Mathematical Problems in Engineering
*

This paper presents a range

doi:10.1155/2015/876862
fatcat:mg6yxlaapbcdrlm74ycgnzxuqi
*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. ...##
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Linearly constrained global optimization via piecewise-linear approximation

2008
*
Journal of Computational and Applied Mathematics
*

solution by solving a set

doi:10.1016/j.cam.2007.02.006
fatcat:5n2f2oawhbaehd3np72efwsvmy
*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. ...##
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Approximate separation of quantum gates and separation experiments of CNOT based on Particle Swarm Optimization algorithm
[article]

2022
*
arXiv
*
pre-print

We propose

arXiv:2201.05786v1
fatcat:wkz74fn7pbh4jmdx7rkcpzlray
*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). ...##
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Design of balanced MBA student teams

2005
*
Journal of the Operational Research Society
*

The

doi:10.1057/palgrave.jors.2601775
fatcat:6ltspgsqsnggdcgheq6ytpmyn4
*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. ...##
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A quadratic programming approach to path smoothing

2011
*
Proceedings of the 2011 American Control Conference
*

Some characteristic nodes

doi:10.1109/acc.2011.5990880
fatcat:rze2pxhpfjcttcwyv4n4yezwcq
*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 . ...##
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Buffer overrun detection using linear programming and static analysis

2003
*
Proceedings of the 10th ACM conference on Computer and communication security - CCS '03
*

We also present fast, scalable solvers based on

doi:10.1145/948109.948155
dblp:conf/ccs/GanapathyJCMV03
fatcat:3e723oqg7vdsfeunmzazkwov5y
*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. ...##
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Buffer overrun detection using linear programming and static analysis

2003
*
Proceedings of the 10th ACM conference on Computer and communication security - CCS '03
*

We also present fast, scalable solvers based on

doi:10.1145/948152.948155
fatcat:jqnz4txfpjb2dchiertyujplwi
*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. ...##
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On Estimation Algorithms vs Approximation Algorithms

2008
*
Foundations of Software Technology and Theoretical Computer Science
*

These algorithms run in polynomial time,

doi:10.4230/lipics.fsttcs.2008.1767
dblp:conf/fsttcs/Feige08
fatcat:ukvanc6yond5jhbmthmgld2gia
*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. ...##
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Linear regression over the max-plus semiring: algorithms and applications
[article]

2017
*
arXiv
*
pre-print

Namely inferring a

arXiv:1712.03499v1
fatcat:7fotyjlrf5ho7d6w3ml5warrzy
*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. ...##
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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 ...

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

2005
*
IFAC Proceedings Volumes
*

The explicit MPC controller is based on an orthogonal search tree structure

doi:10.3182/20050703-6-cz-1902.00826
fatcat:2mitsffdenaujbzpjads5bzmxq
*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 ...##
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AReN: Assured ReLU NN Architecture for Model Predictive Control of LTI Systems
[article]

2019
*
arXiv
*
pre-print

Second, we show that we can efficiently over-

arXiv:1911.01608v1
fatcat:b3vzfghkdjgu5hzyif2ez473lu
*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 ). ...
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