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On Min-Max affine approximants of convex or concave real valued functions from ℝ^k, Chebyshev equioscillation and graphics [article]

Steven B. Damelin, David L. Ragozin, Michael Werman
2021 arXiv   pre-print
We study Min-Max affine approximants of a continuous convex or concave function f:Δ⊂^kℝ where Δ is a convex compact subset of ^k.  ...  In the case when Δ is a simplex we prove that there is a vertical translate of the supporting hyperplane in ^k+1 of the graph of f at the vertices which is the unique best affine approximant to f on Δ  ...  Min-Max approximation In this paper, we are interested in Min-Max approximation to a continuous : Δ ⊂ R − → R by affine approximants to . See for example [4, 3, 7, 9, 11] .  ... 
arXiv:1812.02302v10 fatcat:dx5cchxsb5ftph4emnoq2kynwu

Max-Min k-Dispersion on a Convex Polygon [article]

Vishwanath R. Singireddy, Manjanna Basappa
2022 arXiv   pre-print
Based on the bounded search tree method we propose an exact fixed-parameter algorithm in O(2^k(n^2log n+n(log^2 n)(log k))) time, for this problem, where k is the parameter.  ...  1 > max({r l1 , r l2 } 6 l=1 \ {r 1 }) (b) When r lm * = max {r l1 , r l2 } 6 l=1 and r lm * > r 1 case 2: When r l * m = max {r l1 , r l2 } 6 l=1 and r l * m > r 1 , where l * ∈ {1, 2, . . . , 6}, and  ...  [12] proved that for the max-min k-dispersion problem on an arbitrary weighted graph, we cannot give any constant factor approximation algorithm within polynomial time unless P=NP.  ... 
arXiv:2205.02021v1 fatcat:lsjsjfmqmndnflbfzpeikk6uuu

Weak and strong max-min controllability

M. Heymann, M. Pachter, R. Stern
1976 IEEE Transactions on Automatic Control  
Absstract-Weak and strong max-min controllability for a two player (time-vaqhgl linear control system are defiied. It is proved that the two concepts are equivalent.  ...  The vectors u = u(t) €R"'P and u= u(t) ERm=, regarded. respectively, as the pursuer and ecader controls are required to satisfy J I 11 u(f)l12 dt < ca and J I llc(t)ll2 dt < 00 on each compact interval  ...  Definition I: An event (t,,,xo) in system (1) is wukly max-min confrolluble if for each announced evader control u on [ro_.oo). there exis?  ... 
doi:10.1109/tac.1976.1101275 fatcat:odalrttiubgy7dohxpcf4ny3ha

Max-min control problems: A system theoretic approach

M. Heymann, M. Pachter, R. Stern
1976 IEEE Transactions on Automatic Control  
In this p a p a "max-min controllability" concept for a situation in which two linear control systems are in conflict is introdoced and characterized This concept is employed in solving a max-min linearquadratic  ...  One can readily check that 9 , [ W, (0,3)] = R 3, and hence all events (O,zo) are max-min controllable in time 3. Note, however, that ' 3, [ W,(.i-, 3)] 2 3 [ We(7, 3)] for .i-> 2.  ...  t O ,~p O , x e O ) is max-min controllable, then it is max-min controllable in time T for every T > to.  ... 
doi:10.1109/tac.1976.1101315 fatcat:bpa2rap2afc4vg7nmpfclfprz4

Multicasting MIMO relay optimization based on min-max MSE criterion

Muhammad R. A. Khandaker, Yue Rong
2012 2012 IEEE International Conference on Communication Systems (ICCS)  
In the next section, we optimize the source and relay matrices based on the min-max MSE criterion. III.  ...  matrix optimization problem min T max i tr I N b + T H G H i G i T −1 (14a) s.t. tr(TT H ) ≤ P r (14b) with the high SNR assumption.  ... 
doi:10.1109/iccs.2012.6406100 dblp:conf/iccoms/KhandakerR12 fatcat:xrawylhvvbhazeiu27il7qsbu4

Colour image recognition based on single-layer neural networks of Min/Max nodes

R. Holota
2012 Neural Network World  
An image recognition system can be based on a single-layer neural network composed of Min/Max nodes. This principle is easy to use for greyscale images.  ...  A new modified Min/Max node Single Layer Net, suitable for recognition in HSV (Hue Saturation Value) colour space, is presented in this paper.  ...  One topic of cooperation was focused on single-layer neural nets with Min/Max nodes [5, 1] .  ... 
doi:10.14311/nnw.2012.22.024 fatcat:q5eiyapm3zeklbighrb5fupnke

An application of fuzzy risk analysis based on Max and Min sets

R. Saneifard, H. Hosseini
2014 Communications on Advanced Computational Science with Applications  
The set method of maximizing and minimizing is one of the favorite ranking methods for fuzzy numbers which ranks them on the basis of left and right regions or parts and general applications.  ...  ( ) is monotonic increasing on [a, b], ii. ( ) is monotonic decreasing on [c, b], iii.  ...  When ( ) and R( ) are linear functions and m n, fuzzy number ̃ denotes triangular fuzzy number.  ... 
doi:10.5899/2014/cacsa-00019 fatcat:xrze2ptulrcsjopzqb5aksi3uy

Min-Max Fairness Criteria for Transmission Fixed Cost Allocation

A. R. Abhyankar, S. A. Soman, S. A. Khaparde
2007 IEEE Transactions on Power Systems  
In this paper, we address this complex cost sharing problem by suggesting a min-max fairness algorithm, using optimization-based real power tracing.  ...  The min-max algorithm achieves fairness by equalizing allocations within constrained space and reaching an equilibrium where further balancing cannot be achieved.  ...  Min-Max Fairness for Network Usage Cost Allocation On similar lines of max-min fairness for benefit sharing problem, its variant, the min-max fairness criteria for cost sharing problem, can be proposed  ... 
doi:10.1109/tpwrs.2007.907391 fatcat:bavl7wfftvdcrbvlctmbm2w564

Detecting Communities in Social Networks using Max-Min Modularity [chapter]

Jiyang Chen, Osmar R. Zaïane, Randy Goebel
2009 Proceedings of the 2009 SIAM International Conference on Data Mining  
In this paper, we present a new community mining measure, Max-Min Modularity, which considers both connected pairs and criteria defined by domain experts in finding communities, and then specify a hierarchical  ...  The identification of such communities relies on some notion of clustering or density measure, which defines the communities that can be found.  ...  Based on this criterion, we propose a user-defined community structure measure, we call Max-Min (MM) Modularity.  ... 
doi:10.1137/1.9781611972795.84 dblp:conf/sdm/ChenZG09 fatcat:4odm6piufza7hggm4obtnyjmfu

Extension of Max-Min Ant System with Exponential Pheromone Deposition Rule [article]

Ayan Acharya, Deepyaman Maiti, Aritra Banerjee, R. Janarthanan, Amit Konar
2008 arXiv   pre-print
A roadmap of connected cities, where the shortest path between two specified cities are to be found out, is taken as a platform to compare Max-Min Ant System model (an improved and popular model of Ant  ...  simulations are performed to find the best parameter settings for non-uniform deposition approach and experiments with these parameter settings revealed that the above approach outstripped the traditional one  ...  SIMULATION RESULTS Max-Min Ant System (MMAS) model is considered here to study its performance with two kinds of deposition rules.  ... 
arXiv:0811.0136v1 fatcat:cm76jryqazcorhlr4rwvbq64ju

Max-min transmit beamforming via iterative regularization

Ahmad Gharanjik, M. R. Bhavani Shankar, Mojtaba Soltanalian, Bjorn Ottersten
2016 2016 50th Asilomar Conference on Signals, Systems and Computers  
This paper introduces an iterative optimization framework to tackle the multi-group multicast Max-Min transmit beamforming problem.  ...  Comparison with SDR Method Considering the total power constraint on the signal ( w 2 = 1), P 1 can be equivalently reformulated as R 1 : max . W min i∈[M ] Tr (A i W ) Tr (B i W ) s. t.  ...  [M ], (5) B i (I N − Diag(e i )) ⊗ R i + σ 2 i P I K , ∀i ∈ [M ]. (6) The Max-Min beamforming design problem can then be recast as the following optimization problem: P : max . w∈C K min i∈[M ] w H A i  ... 
doi:10.1109/acssc.2016.7869614 dblp:conf/acssc/GharanjikSSO16 fatcat:ttssz2bjmjevbess3kob3znqca

Max-min Utility Fairness in Link Aggregated Systems

Satya R. Mohanty, Changbin Liu, Bin Liu, Laxmi N. Bhuyan
2007 2007 Workshop on High Performance Switching and Routing  
We consider utility max-min fairness of application traffic of a Next Generation Internet (NGI) service model contending for network bandwidth.  ...  In this paper we only consider max-min fairness. We find it useful to define max-min fairness in a formal manner. A.  ...  PROBLEM FRAMEWORK We consider the utility max-min fairness in an aggregated link environment.  ... 
doi:10.1109/hpsr.2007.4281267 fatcat:xgok4jqiefaxflss7zjcfw67yy

Min-max Graph Partitioning and Small Set Expansion

N. Bansal, U. Feige, R. Krauthgamer, K. Makarychev, V. Nagarajan, J. Naor, R. Schwartz
2011 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science  
We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving  ...  This improves over an O(log 2 n) approximation for the second version due to Svitkina and Tardos [Min-max multiway cut, in APPROX-RANDOM, 2004, Springer, Berlin, 2004], and roughly O(k log n) approximation  ...  , min-max-multiway-cut, and min-max cut in graphs excluding a K r,r -minor, and an improved approximation ratio of O(log g) for the same problems in genus g graphs.  ... 
doi:10.1109/focs.2011.79 dblp:conf/focs/BansalFKMNNS11 fatcat:35lifkfxareixlnlyoradkeroi

Adaptive Max-Min Fair Scheduling in Buffered Crossbar Switches Without Speedup

X. Zhang, S. R. Mohanty, L. N. Bhuyan
2007 IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications  
Index Terms-switch scheduling, buffered crossbar, combined input crosspoint queued (CICQ) switch, quality of service (QoS), max-min fairness.  ...  Then we describe an adaptive maxmin fair scheduling (AMFS) algorithm and show by analysis and simulation that it can provide both 100% throughput and max-min fairness.  ...  To take this situation into consideration, we further introduce a dynamic max-min rate matrix R wλ = [r wλ ij ], based on both W and Λ, whereas the matrix, based only on W , is referred to as static max-min  ... 
doi:10.1109/infcom.2007.60 dblp:conf/infocom/ZhangMB07 fatcat:cuegqxptxza6rnp7j6bdoxptgq

Maximizing Sum Rate and Minimizing MSE on Multiuser Downlink: Optimality, Fast Algorithms and Equivalence via Max-min SINR

Chee Wei Tan, Mung Chiang, R. Srikant
2011 IEEE Transactions on Signal Processing  
We show that, through connections with the nonlinear Perron-Frobenius theory, jointly optimizing power and beamformers in the max-min weighted SINR problem can be solved optimally in a distributed fashion  ...  In the general case, we first establish optimality conditions to the weighted sum MSE minimization and the weighted sum rate maximization problems and provide their further connection to the max-min weighted  ...  By the max-min characterization of 4 : (30) the optimal value of the min-max MSE problem is .  ... 
doi:10.1109/tsp.2011.2165065 fatcat:ukuejnkwg5hwxnkdujm43dliya
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