An implementation of the method of analytic centers

Author(s):  
F. Jarre ◽  
G. Sonnevend ◽  
J. Stoer
Keyword(s):  

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
John Machacek ◽  
Shafiu Jibrin

We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.



2020 ◽  
pp. 129-138
Author(s):  
Arkadii V. Kryazhimskii ◽  
György Sonnevend


2004 ◽  
Vol 29 (1) ◽  
pp. 69-90 ◽  
Author(s):  
Wiesława T. Obuchowska
Keyword(s):  


2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Yusen Wu ◽  
Cui Zhang ◽  
Changjin Xu

With the aid of computer algebra systemMathematica8.0 and by the integral factor method, for a family of generalized nilpotent systems, we first compute the first several quasi-Lyapunov constants, by vanishing them and rigorous proof, and then we get sufficient and necessary conditions under which the systems admit analytic centers at the origin. In addition, we present that seven amplitude limit cycles can be created from the origin. As an example, we give a concrete system with seven limit cycles via parameter perturbations to illustrate our conclusion. An interesting phenomenon is that the exponent parameterncontrols the singular point type of the studied system. The main results generalize and improve the previously known results in Pan.



2021 ◽  
Author(s):  
Alem Fitwi ◽  
Yu Chen ◽  
Sencun Zhu

As smart surveillance becomes popular in today's smart cities, millions of closed circuit television (CCTV) cameras are ubiquitously deployed that collect huge amount of visual information. All these raw visual data are often transported over a public network to distant video analytic centers. This increases the risk of interception and the spill of individuals' information into the wider cyberspace that causes privacy breaches. The edge computing paradigm allows the enforcement of privacy protection mechanisms at the point where the video frames are created. Nonetheless, existing cryptographic schemes are computationally unaffordable at the resource constrained network edge. Based on chaotic methods we propose three lightweight end-to-end (E2E) privacy-protection mechanisms: (1) a Dynamic Chaotic Image Enciphering (DyCIE) scheme that can run in real time at the edge; (2) a lightweight Regions of Interest (RoI) Masking (RoI-Mask) scheme that ensures the privacy of sensitive attributes on video frames; and (3) a novel lightweight Sinusoidal Chaotic Map (SCM) as a robust and efficient solution for enciphering frames at edge cameras. Design rationales are discussed and extensive experimental analyses substantiate the feasibility and security of the proposed schemes.



1982 ◽  
Vol 5 (2) ◽  
pp. 318-328
Author(s):  
Shōji Kobayashi




1995 ◽  
Vol 69 (1-3) ◽  
pp. 45-73 ◽  
Author(s):  
O. Bahn ◽  
O. du Merle ◽  
J. -L. Goffin ◽  
J. -P. Vial


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