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Semidefinite diagonal directions Monte Carlo algorithms for detecting necessary linear matrix inequality constraints
Authors:Shafiu Jibrin  Arnon Boneh  Jackie Van Ryzin
Affiliation:1. Department of Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ 86011-5717, United States;2. The Leon Recanati School of Business Administration, Tel-Aviv University, Ramat Aviv Tel-Aviv 69978, Israel;3. St. Norbert College, De Pere, WI 54115, United States;1. Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA;2. Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX, USA;3. Department of Electrical Engineering, Indian Institute of Science, Bangalore, India;1. LIX, École Polytechnique, 91128 Palaiseau, France;2. IBM, 9 rue de Verdun, 94250 Gentilly, France;1. Centre for Quantum Computation & Intelligent Systems, University of Technology Sydney, Sydney, Australia;2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China;3. Baidu (China) Co., Ltd., Shanghai, China;4. Department of Infrastructure Engineering, University of Melbourne, Melbourne, Australia;1. Institute for Control Sciences RAS, Moscow, Russia;2. Laboratory of Structural Methods of Data Analysis in Predictive Modeling in Moscow Institute of Physics and Technology, Moscow, Russia;1. Research Unit of Automation and Applied Computer (URAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon;2. Research Unit of Condensed Matter, Electronics and Signal Processing (UR-MACETS) Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon;3. Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, Tamilnadu, India;4. Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon;5. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Lodz, Poland
Abstract:Hit-and-run algorithms are Monte Carlo methods for detecting necessary constraints in convex programming including semidefinite programming. The well known of these in semidefinite programming are semidefinite coordinate directions (SCD), semidefinite hypersphere directions (SHD) and semidefinite stand-and-hit (SSH) algorithms. SCD is considered to be the best on average and hence we use it for comparison.We develop two new hit-and-run algorithms in semidefinite programming that use diagonal directions. They are the uniform semidefinite diagonal directions (uniform SDD) and the original semidefinite diagonal directions (original SDD) algorithms. We analyze the costs and benefits of this change in comparison with SCD. We also show that both uniform SDD and original SDD generate points that are asymptotically uniform in the interior of the feasible region defined by the constraints.
Keywords:
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