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Feasible and Accurate Algorithms for Covering Semidefinite Programs [chapter]

Garud Iyengar, David J. Phillips, Cliff Stein
2010 Lecture Notes in Computer Science  
Our algorithms exploit the structural similarity between covering semidefinite programs, packing semidefinite programs and packing and covering linear programs.  ...  In this paper we describe an algorithm to approximately solve a class of semidefinite programs called covering semidefinite programs.  ...  Introduction Semidefinite programming (SDP) is a powerful tool for designing approximation algorithms for NP-hard problems.  ... 
doi:10.1007/978-3-642-13731-0_15 fatcat:x3hqazxt5fctbk4yov2ux5s6e4

Semi-Definite Programming by Perceptron Learning

Thore Graepel, Ralf Herbrich, Andriy Kharechko, John Shawe-Taylor
2003 Neural Information Processing Systems  
We present a modified version of the perceptron learning algorithm (PLA) which solves semidefinite programs (SDPs) in polynomial time.  ...  The algorithm is based on the following three observations: (i) Semidefinite programs are linear programs with infinitely many (linear) constraints; (ii) every linear program can be solved by a sequence  ...  Dunagan, and A. Ambroladze for interesting discussions. This work was supported by EPSRC under grant number GR/R55948 and by Microsoft Research Cambridge.  ... 
dblp:conf/nips/GraepelHKS03 fatcat:rdh4x6ltfne4teqemrsbd2imhq

A Survey of Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics [article]

Anirudha Majumdar, Georgina Hall, Amir Ali Ahmadi
2019 arXiv   pre-print
approximate solutions to semidefinite programs, (iii) more scalable algorithms that rely on augmented Lagrangian techniques and the alternating direction method of multipliers, and (iv) approaches that  ...  Our hope is that this paper will serve as a gateway to the rich and exciting literature on scalable semidefinite programming for both theorists and practitioners.  ...  ACKNOWLEDGMENTS We thank Cemil Dibek for his constructive feedback on the first draft of this manuscript.  ... 
arXiv:1908.05209v3 fatcat:g2vqfhv27vgddbv7l4xciywf4u

Stochastic 0–1 linear programming under limited distributional information

Michael R. Wagner
2008 Operations Research Letters  
We give a robust formulation, as a function of k, for the 0-1 integer linear program under this limited distributional information.  ...  Finally, this research was made possible, in part, by financial support from the Office of Research and Sponsored Programs at California State University East Bay.  ...  We would also like to thank Ioana Popescu for reading an early draft and providing constructive feedback.  ... 
doi:10.1016/j.orl.2007.07.003 fatcat:svb2gfjq3jgblj3m3gspo7xfdi

Sparse Semidefinite Programs with Guaranteed Near-Linear Time Complexity via Dualized Clique Tree Conversion [article]

Richard Y. Zhang, Javad Lavaei
2020 arXiv   pre-print
Assuming that ω≪ n, we prove that the per-iteration cost of an interior-point method is linear O(n) time and memory, so an ϵ-accurate and ϵ-feasible iterate is obtained after O(√(n)log(1/ϵ)) iterations  ...  We consider two classes of semidefinite programs with favorable sparsity patterns that encompass the MAXCUT and MAX k-CUT relaxations, the Lovasz Theta problem, and the AC optimal power flow relaxation  ...  Our first main result guarantees these complexity figures for a class of semidefinite programs that we call partially separable semidefinite programs.  ... 
arXiv:1710.03475v4 fatcat:l7kwecoftnhj5ire5nbk6cktdm

Semidefinite Programming and Integer Programming [chapter]

Monique Laurent, Franz Rendl
2005 Handbooks in Operations Research and Management Science  
We thank a referee for his careful reading and his suggestions that helped improve the presentation of this chapter.  ...  the feasibility region of a semidefinite program (3) .  ...  A prominent part covers semidefinite programming and combinatorial optimization. http://www.optimization-online.org The semidefinite programming web-site maintained by C.  ... 
doi:10.1016/s0927-0507(05)12008-8 fatcat:ez23hvr5znfolnppcugzpevgpu

On verified numerical computations in convex programming

Christian Jansson
2009 Japan journal of industrial and applied mathematics  
Especially, we consider the computation of verified error bounds for non-smooth convex conic optimization in the framework of functional analysis, for linear programming, and for semidefinite programming  ...  The latter are important for handling and for reliability issues in global robust and combinatorial optimization.  ...  Most of the applications are covered by linear programming and semidefinite programming(SDP).  ... 
doi:10.1007/bf03186539 fatcat:epentouc4bgm7azndvdwlfzpdy

A New Conic Approach to Semisupervised Support Vector Machines

Ye Tian, Jian Luo, Xin Yan
2016 Mathematical Problems in Engineering  
Anϵ-optimal solution can be found in finite iterations using semidefinite programming techniques by our method.  ...  The numerical results show that the proposed algorithm can achieve more accurate classifications than other well-known conic relaxations of semisupervised support vector machine models in the literature  ...  Acknowledgments Tian's research has been supported by the National Natural Science Foundation of China Grants 11401485 and 71331004.  ... 
doi:10.1155/2016/6471672 fatcat:2kh2yiilc5fhtfgphpi7pa4khy

Using Algebraic Properties of Minimal Idempotents for Exhaustive Computer Generation of Association Schemes

K. Coolsaet, J. Degraer
2008 Electronic Journal of Combinatorics  
Central to our success is the use of two algebraic constraints based on properties of the minimal idempotents $E_{i}$ of these association schemes : the fact that they are positive semidefinite and that  ...  Incorporating these constraints into an actual isomorph-free exhaustive generation algorithm turns out to be somewhat complicated in practice.  ...  A less accurate implementation of Algorithm 2 simply results in a less efficient generation program.  ... 
doi:10.37236/754 fatcat:ddilpk2ej5dybel2q7z4gcnbzm

A semidefinite programming approach for cooperative localization

Ning Wang, Liuqing Yang
2010 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers  
This is why a cooperative TDoA algorithm is not covered in this thesis.  ...  Minimax SDP Algorithm Analysis Generally speaking, rank-d algorithms are in a suitable style for cooperative localization with accurate performances and are recommended for its convenient reformulation  ... 
doi:10.1109/acssc.2010.5757606 fatcat:5fjzpdgzvjddpofo7vpsu3zgza

An introduction to convex optimization for communications and signal processing

Zhi-Quan Luo, Wei Yu
2006 IEEE Journal on Selected Areas in Communications  
Special emphasis is placed on a class of conic optimization problems, including second-order cone programming and semidefinite programming.  ...  Convex optimization methods are widely used in the design and analysis of communication systems and signal processing algorithms. This tutorial surveys some of recent progress in this area.  ...  CONIC PROGRAMMING FOR MULTIUSER BEAMFORMING The rest of this paper treats several applications of convex optimization in communications and signal processing to illustrate the concepts covered so far.  ... 
doi:10.1109/jsac.2006.879347 fatcat:texfpv6c7vgmniuso444hxxham

On fractional cut covers

José Neto, Walid Ben-Ameur
2019 Discrete Applied Mathematics  
A general randomized approach is also presented giving new insights into Goemans and Williamson's algorithm for the maximum cut problem.  ...  Given an undirected graph, a minimum cut cover is a collection of cuts covering the whole set of edges and having minimum cardinality.  ...  Acknowledgments The authors are grateful to the editors and anonymous referees for their helpful suggestions that greatly improved the quality of the paper.  ... 
doi:10.1016/j.dam.2019.03.020 fatcat:w6xq3twkbraabkj5q3n4qo4jna

Regression From Uncertain Labels and Its Applications to Soft Biometrics

Shuicheng Yan, Huan Wang, Xiaoou Tang, Jianzhuang Liu, Thomas S. Huang
2008 IEEE Transactions on Information Forensics and Security  
Two transformation matrices are then learned for deriving such a matrix by solving two semidefinite programming (SDP) problems, in which the uncertain label of each sample is expressed as two inequality  ...  algorithmic generalization capability.  ...  The semidefinite programming toolbox can be applied for the step-wise optimization. B.  ... 
doi:10.1109/tifs.2008.2006585 fatcat:kkj6ydw76fgetm5jxmisl2lbje

SDP-Based Bounds for the Quadratic Cycle Cover Problem via Cutting-Plane Augmented Lagrangian Methods and Reinforcement Learning

Frank de Meijer, Renata Sotirov
2021 INFORMS journal on computing  
We derive several semidefinite programming (SDP) relaxations and use facial reduction to make these strictly feasible.  ...  In this paper, we study the application of semidefinite programming (SDP) to obtain strong bounds for the QCCP.  ...  The authors also thank Dion Gijswijt for carefully reading the manuscript and giving his valuable feedback. Moreover, the authors thank Borzou Rostami for sharing the reload instances.  ... 
doi:10.1287/ijoc.2021.1075 fatcat:5lhweboaivhhvpmbfpcy4mxzwy

Definable Ellipsoid Method, Sums-of-Squares Proofs, and the Isomorphism Problem

Albert Atserias, Joanna Ochremiak
2018 Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '18  
We use this observation to show that the exact feasibility problem for semidefinite programs is expressible in the infinitary version of FPC.  ...  The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem.  ...  We are grateful to Christoph Berkholz, Anuj Dawar, and Wied Pakusa, for useful discussions at an early stage of this work.  ... 
doi:10.1145/3209108.3209186 dblp:conf/lics/AtseriasO18 fatcat:4pxjokuxwzch5oakuwube2l7j4
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