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Low-Rank Semidefinite Programming

This monograph reviews the theory of low-rank semidefinite programming, presenting theorems that guarantee the existence of a low-rank solution, heuristics for computing low-rank solutions, and algorithms for finding low-rank approximate ...

Author : Alex Lemon

Release : 2016-05-04

Publisher : Now Publishers

ISBN : 9781680831368

File Size : 62.31 MB

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Finding low-rank solutions of semidefinite programs is important in many applications. For example, semidefinite programs that arise as relaxations of polynomial optimization problems are exact relaxations when the semidefinite program has a rank-1 solution. Unfortunately, computing a minimum-rank solution of a semidefinite program is an NP-hard problem. This monograph reviews the theory of low-rank semidefinite programming, presenting theorems that guarantee the existence of a low-rank solution, heuristics for computing low-rank solutions, and algorithms for finding low-rank approximate solutions. It then presents applications of the theory to trust-region problems and signal processing.

Low-Rank and Sparse Modeling for Visual Analysis

9, 1019–1048 (2008) S. Burer, R. Monteiro, Local minima and convergence in
low-rank semidefinite programming. Math. Program. 103,427–444 (2005) J. Cai,
S. Osher, Fast singular value thresholding without singular value decomposition.

Author : Yun Fu

Release : 2014-10-30

Publisher : Springer

ISBN : 331912000X

File Size : 24.4 MB

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This book provides a view of low-rank and sparse computing, especially approximation, recovery, representation, scaling, coding, embedding and learning among unconstrained visual data. The book includes chapters covering multiple emerging topics in this new field. It links multiple popular research fields in Human-Centered Computing, Social Media, Image Classification, Pattern Recognition, Computer Vision, Big Data, and Human-Computer Interaction. Contains an overview of the low-rank and sparse modeling techniques for visual analysis by examining both theoretical analysis and real-world applications.

Handbook of Robust Low-Rank and Sparse Matrix Decomposition

Local minima and convergence in low-rank semidefinite programming.
Mathematical Programming, 103(3):427–444, December 2005. 7. N. Campbell.
Robust procedures in multivariate analysis i: Robust covariance estimation.
Applied Stat.

Author : Thierry Bouwmans

Release : 2016-09-20

Publisher : CRC Press

ISBN : 1498724639

File Size : 59.5 MB

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Handbook of Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing shows you how robust subspace learning and tracking by decomposition into low-rank and sparse matrices provide a suitable framework for computer vision applications. Incorporating both existing and new ideas, the book conveniently gives you one-stop access to a number of different decompositions, algorithms, implementations, and benchmarking techniques. Divided into five parts, the book begins with an overall introduction to robust principal component analysis (PCA) via decomposition into low-rank and sparse matrices. The second part addresses robust matrix factorization/completion problems while the third part focuses on robust online subspace estimation, learning, and tracking. Covering applications in image and video processing, the fourth part discusses image analysis, image denoising, motion saliency detection, video coding, key frame extraction, and hyperspectral video processing. The final part presents resources and applications in background/foreground separation for video surveillance. With contributions from leading teams around the world, this handbook provides a complete overview of the concepts, theories, algorithms, and applications related to robust low-rank and sparse matrix decompositions. It is designed for researchers, developers, and graduate students in computer vision, image and video processing, real-time architecture, machine learning, and data mining.

Modeling and Optimization of Interdependent Energy Infrastructures

Maher, A.: Semidefinite programming: methods and algorithms for energy
management. Working Paper ... 143(1), 1–29 (2014) Burer, S., Monteiro, R.D.C.:
Local minima and convergence in low-rank semidefinite programming. Math.
Program.

Author : Wei Wei

Release : 2019-10-22

Publisher : Springer Nature

ISBN : 3030259587

File Size : 80.69 MB

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This book opens up new ways to develop mathematical models and optimization methods for interdependent energy infrastructures, ranging from the electricity network, natural gas network, district heating network, and electrified transportation network. The authors provide methods to help analyze, design, and operate the integrated energy system more efficiently and reliably, and constitute a foundational basis for decision support tools for the next-generation energy network. Chapters present new operation models of the coupled energy infrastructure and the application of new methodologies including convex optimization, robust optimization, and equilibrium constrained optimization. Four appendices provide students and researchers with helpful tutorials on advanced optimization methods: Basics of Linear and Conic Programs; Formulation Tricks in Integer Programming; Basics of Robust Optimization; Equilibrium Problems. This book provides theoretical foundation and technical applications for energy system integration, and the the interdisciplinary research presented will be useful to readers in many fields including electrical engineering, civil engineering, and industrial engineering.

Learning Approaches in Signal Processing

L. Vandenberghe and S. Boyd, Semidefinite programming, SIAM Rev., vol. 38, no
. 1, pp. 49–95, 1996. 9. A. Lemon, A. M.-C. So, and Y. Ye, Low-rank semidefinite
programming: Theory and applications,Found. Trends Optim., vol. 2, no. 1–2, pp.

Author : Wan-Chi Siu

Release : 2018-12-07

Publisher : CRC Press

ISBN : 0429592264

File Size : 45.14 MB

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Coupled with machine learning, the use of signal processing techniques for big data analysis, Internet of things, smart cities, security, and bio-informatics applications has witnessed explosive growth. This has been made possible via fast algorithms on data, speech, image, and video processing with advanced GPU technology. This book presents an up-to-date tutorial and overview on learning technologies such as random forests, sparsity, and low-rank matrix estimation and cutting-edge visual/signal processing techniques, including face recognition, Kalman filtering, and multirate DSP. It discusses the applications that make use of deep learning, convolutional neural networks, random forests, etc. The applications include super-resolution imaging, fringe projection profilometry, human activities detection/capture, gesture recognition, spoken language processing, cooperative networks, bioinformatics, DNA, and healthcare.

Advances in Neural Information Processing Systems 19

for. Large-Scale. Semidefinite. Programming. Kilian Q. Weinberger Fei Sha Dept
of Computer and Information Science ... In particular, many results have been
obtained by constructing semidefinite programs (SDPs) with low rank solutions.

Author : Bernhard Schölkopf

Release : 2007

Publisher : MIT Press

ISBN : 0262195682

File Size : 34.26 MB

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The annual conference on NIPS is the flagship conference on neural computation. It draws top academic researchers from around the world & is considered to be a showcase conference for new developments in network algorithms & architectures. This volume contains all of the papers presented at NIPS 2006.

ESAIM.

Author :

Release : 2007

Publisher :

ISBN :

File Size : 76.48 MB

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Scalable Convex Optimization Methods for Semidefinite Programming

Mots-clés de l'auteur: Convex optimization ; semidefinite programming ; low-rank matrix optimization ; primal-dual methods ; conditional gradient methods ; low-rank matrix sketching.

Author : Alp Yurtsever

Release : 2019

Publisher :

ISBN :

File Size : 84.4 MB

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Mots-clés de l'auteur: Convex optimization ; semidefinite programming ; low-rank matrix optimization ; primal-dual methods ; conditional gradient methods ; low-rank matrix sketching.

INFORMS Conference Program

We show that surprisingly one can recover low - rank matrices exactly from what
appear to be highly incomplete sets of entries . Further , perfect recovery is
possible by solving a semidefinite program . Our methods are optimal and
succeed as ...

Author : Institute for Operations Research and the Management Sciences. National Meeting

Release : 2009

Publisher :

ISBN :

File Size : 32.95 MB

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Mathematical Reviews

Summary : “ In this paper , we present an interior - point algorithm for large and
sparse convex quadratic programming ... The proof uses results on the existence
of low - rank solutions to positive semidefinite programs ( see A . I . Barvinok ...

Author :

Release : 2007

Publisher :

ISBN :

File Size : 65.71 MB

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A Semidefinite Programming Approach to the Graph Realization Problem

... we take a step back and consider the Graph Realization Problem in a broader
context , namely that of rank - constrained semidefinite programming . Indeed ...
However , for a general system of linear matrix equations , a low - rank solution ...

Author : Anthony Man-Cho So

Release : 2007

Publisher :

ISBN :

File Size : 83.10 MB

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Dissertation Abstracts International

For freeware , a usage tax is the most effective policy except when both patching
costs and security risk are low , in which ... Adviser : Samuel Burer Order Number
DA3265938 The low - rank semidefinite programming solver SDPLR , originally ...

Author :

Release : 2007

Publisher :

ISBN :

File Size : 90.21 MB

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日本オペレーションズ・リサーチ学会論文誌

( 5 ) S . Burer and R . Monteiro : A nonlinear programming algorithm for solving
semidefinite programs via low - rank ... ( 6 ) E . Cancès , G . Stoltz and M . Lewin :
The electronic ground - state energy problem : A new reduced density matrix ...

Author : 日本オペレーションズ・リサーチ学会

Release : 2007

Publisher :

ISBN :

File Size : 70.36 MB

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SPAWC

... Low - Rank Relaxation The MIMO channel is modeled as a single - user
wireless The constellation points for general ... transmitted by antenna i ,
optimization as a low - rank semi - definite programming relaxrelaxation was first
considered in ...

Author :

Release : 2003

Publisher :

ISBN :

File Size : 84.9 MB

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Parallel Combinatorial Optimization

A nonlinear programming algorithm for solving semidefinite programs via low -
rank factorization . Math . Prog . ( Ser . B ) , 95 ( 2 ) : 329 – 357 ( 2003 ) . 24 . C .
Helmberg and F . Rendl . A spectral bundle method for semidefinite programming
.

Author : Talbi

Release : 2006-10-13

Publisher : Wiley-Interscience

ISBN :

File Size : 71.11 MB

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Learn to solve complex problems with efficient parallel optimization algorithms This text provides an excellent balance of theory and application that enables readers to deploy powerful algorithms, frameworks, and methodologies to solve complex optimization problems in a diverse range of industries. Each chapter is written by leading experts in the fields of parallel and distributed optimization. Collectively, the contributions serve as a complete reference to the field of combinatorial optimization, including details and findings of recent and ongoing investigations. Readers learn to solve large-scale problems quickly and efficiently with the text's clear coverage of several parallel optimization algorithms: Exact algorithms, including branch and bound, dynamic programming, branch and cut, semidefinite programming, and constraint programming Metaheuristics, including local search, tabu search, simulated annealing, scatter search, GRASP, variable neighborhood search, ant colonies, genetic programming, evolution strategies, and genetic algorithms Hybrid approaches, combining exact algorithms and metaheuristics Multi-objective optimization algorithms The text not only presents parallel algorithms and applications, but also software frameworks and libraries that integrate parallel algorithms for combinatorial optimization. Among the well-known parallel and distributed frameworks covered are COIN, ParadisEO, BOB++, MW, and SDPARA. Numerous real-world examples of problems and solutions demonstrate how parallel combinatorial optimization is applied in such fields as telecommunications, logistics, genomics, networking, and transportation. Whether you are a practicing engineer, field researcher, or student, this text provides you with not only the theory of parallel combinatorial optimization, but the guidance and practical tools to solve complex problems using powerful algorithms.

SIAM Journal on Scientific Computing

[ 3 ] S . J . BENSON , Y . YE , AND X . ZHANG , Solving large - scale sparse
semidefinite programs for combinatorial ... D . C . MONTEIRO , A nonlinear
programming algorithm for solving semidefinite programs via low - rank
factorization , Math .

Author :

Release : 2009

Publisher :

ISBN :

File Size : 85.59 MB

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Structured Primal-dual Interior-point Methods for Semidefinite Programming

Table 3.1 : Numerical rank of intermediate matrices Matrix Ak U AZ AX Rank T (
Sx ) + 2w 37 ( Sx ) + 2w W AX , 47 ( Sx ) + 3w ... We expect that F ( Sx ) has low
rank , approximately equal tow , if the solution pair is close enough to the u -
center ...

Author : Zhiming Deng

Release : 2008

Publisher :

ISBN :

File Size : 67.84 MB

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Information Technology Applications in Industry

Based on the semidefinite programming relaxation of the design of FIR digital
filters with SP2 coefficients, a feasible ... on the low-rank decomposition, Liu [12]
proposed a feasible direction method to solve a nonlinear programming model of
 ...

Author : Jun Zhang

Release : 2012-12-27

Publisher : Trans Tech Publications Ltd

ISBN : 3038139556

File Size : 55.76 MB

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The present book includes selected papers from the 2012 International Conference on Information Technology and Management Innovation (ICITMI 2012), held in Guangzhou, from 10 to 11 November 2012. Volume is indexed by Thomson Reuters CPCI-S (WoS). These selected papers reflect the interdisciplinary nature of the conference and the diversity of topics is an important feature of this conference, enabling an overall perception of several important scientific and technological trends.

Verification, Model Checking, and Abstract Interpretation

Approximating the domains of functional and imperative programs . Sci . Comput
. Programming , 35 ( 1 ) : 113 – 136 , 1999 . 4 . S . Burer and R . Monteiro . A
nonlinear programming algorithm for solving semidefinite programs via low - rank
 ...

Author :

Release : 2005

Publisher :

ISBN :

File Size : 37.51 MB

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Algorithms –- ESA 2012

The framework employs an approximative semidefinite program solver for a fixed
parameter value. Here we ... Hazan's algorithm scales well to large inputs,
provides low-rank approximate solutions with guarantees, and only needs a
simple ...

Author : Leah Epstein

Release : 2012-08-30

Publisher : Springer

ISBN : 3642330908

File Size : 61.66 MB

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This book constitutes the refereed proceedings of the 20th Annual European Symposium on Algorithms, ESA 2012, held in Ljubljana, Slovenia, in September 2012 in the context of the combined conference ALGO 2012. The 69 revised full papers presented were carefully reviewed and selected from 285 initial submissions: 56 out of 231 in track design and analysis and 13 out of 54 in track engineering and applications. The papers are organized in topical sections such as algorithm engineering; algorithmic aspects of networks; algorithmic game theory; approximation algorithms; computational biology; computational finance; computational geometry; combinatorial optimization; data compression; data structures; databases and information retrieval; distributed and parallel computing; graph algorithms; hierarchical memories; heuristics and meta-heuristics; mathematical programming; mobile computing; on-line algorithms; parameterized complexity; pattern matching, quantum computing; randomized algorithms; scheduling and resource allocation problems; streaming algorithms.