An implementation of the method of analytic centers

2006 ◽  
pp. 295-308 ◽  
Author(s):  
F. Jarre ◽  
G. Sonnevend ◽  
J. Stoer
Keyword(s):  
Analytic Centers

scholarly journals An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
John Machacek ◽  
Shafiu Jibrin
Keyword(s):  
Newton’S Method ◽  
Interior Point ◽  
Newton's Method ◽  
Interior Point Method ◽  
Optimal Solution ◽  
Point Method ◽  
Feasible Region ◽  
Test Problems ◽  
Analytic Centers ◽  
Semidefinite Programs

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.

Dynamics for Bimatrix Games Via Analytic Centers

2020 ◽  
pp. 129-138
Author(s):  
Arkadii V. Kryazhimskii ◽  
György Sonnevend
Keyword(s):  
Bimatrix Games ◽  
Analytic Centers

Remarks on the Analytic Centers of Convex Sets

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

scholarly journals Limit Cycles and Analytic Centers for a Family of4n-1Degree Systems with Generalized Nilpotent Singularities

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Yusen Wu ◽  
Cui Zhang ◽  
Changjin Xu
Keyword(s):  
Limit Cycles ◽  
Computer Algebra System ◽  
Necessary Conditions ◽  
Rigorous Proof ◽  
Analytic Centers ◽  
Interesting Phenomenon ◽  
Parameter Perturbations ◽  
Sufficient And Necessary Conditions ◽  
Lyapunov Constants ◽  
Point Type

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.

scholarly journals Lightweight Frame Scrambling Mechanisms for End-to-End Privacy in Edge Smart Surveillance

2021 ◽  
Author(s):  
Alem Fitwi ◽  
Yu Chen ◽  
Sencun Zhu
Keyword(s):  
Privacy Protection ◽  
Visual Information ◽  
Smart Cities ◽  
Chaotic Map ◽  
Analytic Centers ◽  
Public Network ◽  
Video Frames ◽  
Smart Surveillance ◽  
Protection Mechanisms ◽  
End To End

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.

scholarly journals On analytic centers of compact sets

1982 ◽  
Vol 5 (2) ◽  
pp. 318-328
Author(s):  
Shōji Kobayashi
Keyword(s):  
Compact Sets ◽  
Analytic Centers

A method of Analytic Centers for Quadratically Constrained Convex Quadratic Programs

1991 ◽  
Vol 28 (2) ◽  
pp. 529-544 ◽  
Author(s):  
Sanjay Mehrotra ◽  
Jie Sun
Keyword(s):  
Analytic Centers ◽  
Quadratic Programs ◽  
Quadratically Constrained

A cutting plane method from analytic centers for stochastic programming

1995 ◽  
Vol 69 (1-3) ◽  
pp. 45-73 ◽  
Author(s):  
O. Bahn ◽  
O. du Merle ◽  
J. -L. Goffin ◽  
J. -P. Vial
Keyword(s):  
Stochastic Programming ◽  
Cutting Plane ◽  
Cutting Plane Method ◽  
Analytic Centers ◽  
Plane Method
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