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A scaling-invariant algorithm for linear programming whose running time depends only on the constraint matrix

Daniel Dadush, Sophie Huiberts, Bento Natura, László A. Végh
2020 Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing  
Prog. '96) gave the first exact algorithm for linear programming in the real model of computation with running time depending only on the constraint matrix.  ...  Optim. '03), noting that the central path is invariant under rescalings of the columns of A and c, asked whether there exists an LP algorithm depending instead on the measureχ * A , defined as the minimumχ  ...  Kitahara and Tsuchiya [20] , gave a 2-layer LLS step which achieves a running time depending only on χ * A and right-hand side b, but with no dependence on the objective, assuming the primal feasible  ... 
doi:10.1145/3357713.3384326 dblp:conf/stoc/DadushHNV20 fatcat:uu3prpzr6vddvemgnxjsbgo5sm

Scale and rotation invariant matching using linearly augmented trees

Hao Jiang, Tai-Peng Tian, Stan Sclaroff
2011 CVPR 2011  
We propose a novel linearly augmented tree method for efficient scale and rotation invariant object matching.  ...  The pairwise constraints admit arbitrary metrics while the high-order constraints use L1 norms and therefore can be linearized.  ...  Complexity: The complexity of the proposed method depends on the tree structure matching and the linear programming for fusing the proposals.  ... 
doi:10.1109/cvpr.2011.5995580 dblp:conf/cvpr/JiangTS11 fatcat:o4ztnnrjizaabbp5kcqoel2wre

Scale and Rotation Invariant Matching Using Linearly Augmented Trees

Hao Jiang, Tai-Peng Tian, Stan Sclaroff
2015 IEEE Transactions on Pattern Analysis and Machine Intelligence  
We propose a novel linearly augmented tree method for efficient scale and rotation invariant object matching.  ...  The pairwise constraints admit arbitrary metrics while the high-order constraints use L1 norms and therefore can be linearized.  ...  The average running time for optimization in one frame is measured on a 2.8GHZ machine. shown in Fig. 10 and Fig. 11 respectively.  ... 
doi:10.1109/tpami.2015.2409880 pmid:26539858 fatcat:24sm6jyp2zhaxptppcldi7n4ha

The Nonlinear Geometry of Linear Programming. I Affine and Projective Scaling Trajectories

D. A. Bayer, J. C. Lagarias
1989 Transactions of the American Mathematical Society  
A basic feature of the projective scaling algorithm is a vector field depending on the objective function which is defined on the interior of the polytope of feasible solutions of the linear program.  ...  As a consequence there is a polynomial time linear programming algorithm using the affine scaling vector field of this associated linear program: This algorithm is essentially Karmarkar's algorithm.  ...  Vaidya [Va] and Gonzaga [Go] obtain worst-case running-time bounds that improve on Karmarkar by a factor of >fm, where m denotes the number of inequality constraints on the linear program.  ... 
doi:10.2307/2001396 fatcat:adzqmfrefjchnf7gqpjsxlajoq

Object matching with a locally affine-invariant constraint

Hongsheng Li, Edward Kim, Xiaolei Huang, Lei He
2010 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition  
In this paper, we present a new object matching algorithm based on linear programming and a novel locally affine-invariant geometric constraint.  ...  This is a major difficulty for this kind of matching algorithms.  ...  Hao Jiang (Boston College) for providing us the code of [10] for comparison and for giving us precious suggestions on efficient trust-region-shrinkage algorithms.  ... 
doi:10.1109/cvpr.2010.5539776 dblp:conf/cvpr/LiKHH10 fatcat:r4hbt2jlpzfdjgj6lauwwgq4d4

numpywren: serverless linear algebra [article]

Vaishaal Shankar, Karl Krauth, Qifan Pu, Eric Jonas, Shivaram Venkataraman, Ion Stoica, Benjamin Recht, Jonathan Ragan-Kelley
2018 arXiv   pre-print
However, it is challenging for scientists and data analysts to run linear algebra at scales beyond a single machine.  ...  We present numpywren, a system for linear algebra built on a serverless architecture.  ...  We would like to thank Horia Mania, Alyssa Morrow and Esther Rolf for helpful comments while writing this paper.  ... 
arXiv:1810.09679v1 fatcat:lxv65s42rzd6vomkg2pff2akhm

The nonlinear geometry of linear programming. I. Affine and projective scaling trajectories

D. A. Bayer, J. C. Lagarias
1989 Transactions of the American Mathematical Society  
A basic feature of the projective scaling algorithm is a vector field depending on the objective function which is defined on the interior of the polytope of feasible solutions of the linear program.  ...  As a consequence there is a polynomial time linear programming algorithm using the affine scaling vector field of this associated linear program: This algorithm is essentially Karmarkar's algorithm.  ...  Vaidya [Va] and Gonzaga [Go] obtain worst-case running-time bounds that improve on Karmarkar by a factor of >fm, where m denotes the number of inequality constraints on the linear program.  ... 
doi:10.1090/s0002-9947-1989-1005525-6 fatcat:a7eoqldvvba6vnkcnry2qtu3xy

Nearly Linear-Work Algorithms for Mixed Packing/Covering and Facility-Location Linear Programs [article]

Neal E. Young
2014 arXiv   pre-print
We describe the first nearly linear-time approximation algorithms for explicitly given mixed packing/covering linear programs, and for (non-metric) fractional facility location.  ...  The algorithms compute (1+ϵ)-approximate solutions in time (and work) O^*(N/ϵ^2), where N is the number of non-zeros in the constraint matrix.  ...  We give the first nearly linear-time (1 + ǫ)-approximation algorithms and the first nearly linear-work parallel algorithms for mixed packing/covering linear programs and for fractional facility location  ... 
arXiv:1407.3015v3 fatcat:lepw5segbrdu7h4fuip3yau4ke

Linear Programming Heuristics for the Graph Isomorphism Problem [article]

Reza Takapoui, Stephen Boyd
2016 arXiv   pre-print
In this paper we introduce effective probabilistic linear programming (LP) heuristics to solve the graph isomorphism problem.  ...  An isomorphism between two graphs is a bijection between their vertices that preserves the edges.  ...  Recently, Babai announced a quasipolynomial time algorithm for all graphs, i.e., one with running time 2 O((log n) c ) for some fixed c > 0 [Bab15] .  ... 
arXiv:1611.00711v1 fatcat:tucelxqrcfdalg5zh5vbfb7bpq

Parallel Explicit Model Predictive Control [article]

Yuning Jiang, Juraj Oravec, Boris Houska, Michal Kvasnica
2019 arXiv   pre-print
This paper is about a real-time model predictive control (MPC) algorithm for large-scale, structured linear systems with polytopic state and control constraints.  ...  The feedback controller is suboptimal on purpose because we are enforcing real-time requirements assuming that it is impossible to solve the given large-scale QP in the given amount of time.  ...  Acknowledgements The authors thank three anonymous reviewers and the associate editor for their precise and substantial remarks, which have helped to significantly improve this article.  ... 
arXiv:1903.06790v1 fatcat:3mc2sov7cvfotocy6f5cmqz5au

Invariant, Viability and Discriminating Kernel Under-Approximation via Zonotope Scaling [article]

Ian M. Mitchell and Jacob Budzis and Andriy Bolyachevets
2019 arXiv   pre-print
The results are demonstrated on two toy examples and a six dimensional nonlinear longitudinal model of a quadrotor.  ...  Given a set of state and input constraints, and treating the inputs in best-case and/or worst-case fashion, we construct invariant, viable and discriminating sets, which must therefore under-approximate  ...  Run time for the optimization is just over 5 minutes. Only 11 of the 48 generators achieved a scaling factor γ i ≥ 0.01. Figure 8 shows projections of the resulting discriminating set.  ... 
arXiv:1901.01006v1 fatcat:akffqki5dngxni7gayttextxqq

Speeding Up Logico-Numerical Strategy Iteration (extended version) [article]

David Monniaux, Peter Schrammel
2014 arXiv   pre-print
Template polyhedral analysis abstracts numerical variables inside a program by one polyhedron per control location, with a priori fixed directions for the faces.  ...  Unfortunately, the above approaches lead to unacceptable space and time costs if applied to a program whose control states have been partitioned according to predicates.  ...  The research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP7/20072013) / ERC grant agreement 306595 "STATOR"  ... 
arXiv:1403.2319v2 fatcat:5skr4iixbbdgnnsla755whel3i

Invariant Generation through Strategy Iteration in Succinctly Represented Control Flow Graphs

Thomas Gawlitza, David Monniaux, Gilles Barthe
2012 Logical Methods in Computer Science  
We consider the problem of computing numerical invariants of programs, for instance bounds on the values of numerical program variables.  ...  Formally speaking, our technique computes the least fixpoint within a given template linear constraint domain of a transition relation that is succinctly expressed as an existentially quantified linear  ...  Acknowledgments The authors wish to thank the anonymous referees for their helpful suggestions and references.  ... 
doi:10.2168/lmcs-8(3:29)2012 fatcat:daswv22kazh2xdk67ftzit4nze

A global piecewise smooth Newton method for fast large-scale model predictive control

Panagiotis Patrinos, Pantelis Sopasakis, Haralambos Sarimveis
2011 Automatica  
In this paper, the strictly convex quadratic program (QP) arising in model predictive control for constrained linear systems is reformulated as a system of piecewise affine equations.  ...  The proposed algorithm is orders of magnitudes faster, especially for large-scale problems and long horizons.  ...  However, for large-scale linear systems it is prohibitive to compute a polyhedral terminal invariant set, such as the maximal positive invariant set corresponding to the system in closed loop with the  ... 
doi:10.1016/j.automatica.2011.05.024 fatcat:nbbrdrlhcjfaze64jxs3jya7zi

Maximal Invariant Set Computation and Design for Markov Chains [article]

Dylan Janak, Behçet Açıkmeşe
2019 arXiv   pre-print
We describe an algorithm for computing the maximal invariant set for a Markov chain with linear safety constraints on the distribution over states.  ...  Although this problem is bilinear in the general case, we are able to optimize the convergence rate to a desirable steady-state distribution over reversible Markov chains by solving a Semidefinite Program  ...  For a time-invariant Markov chain x + = M x, the problem of reducing safety constraints Gx[k] ≤ g, ∀k ≥ 0 to a set of conditions that depends only on x[0] is equivalent to computing the maximal positively  ... 
arXiv:1905.00947v1 fatcat:huc2tp4t4rhkjfrbmhw5gwymf4
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