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Dr. Richard Caron

Professor of Mathematics and Statistics
Cross Appointed to Computer Science
Industrial and Manufacturing Systems Engineering Doctoral Program


Department Head

B.M., M.M., Ph.D. (Waterloo)
LT 10-111
Ext. 5055

Email: rcaron@uwindsor.ca

Url: /rcaron

 

Area of Research:Mathematical Optimization and Operational Research.

Research Interests:Dr. Caron’s main research focus is on the representation of feasibility regions for mathematical programs. Specifically, he is concerned with the characterization of minimal representations and with the development of algorithms, particularly probabilistic algorithms, to determine such a minimal representation. This area of research includes the development of probabilistic algorithms to find feasibility and for related problems in computational geometry, such as algorithms for extreme point identification. Dr. Caron is also working with colleagues in Industrial Engineering on the application of operational research techniques for hospital administration.  Dr. Caron has successfully supervised 18 master’s students and 3 doctoral students; and is currently supervising a master’s student in mathematics, a master’s student in industrial engineering, and a doctoral student in computer science.

Potential Graduate Student Projects: 

  • Probabilistic feasibility algorithms for nonlinear convex optimization problems.
  • Probabilistic algorithms for integer programming problems.
  • Matrix inversion free interior point algorithms for convex quadratic programming.
  • Probabilistic algorithms for the analysis of sets of constraints.

Dr. Caron has the following graduate students currently under his supervision.

Kevin Durda (PhD. Computer Science, Co-supervised with L. Buchanan)

Jing Shao (MSc, Mathematics, co-supervised with Dr. Myron Hlynka)

Mike Lee (MSc, Mathematics)

Dr. Caron has successfully supervised 19 master’s students and 3 doctoral students. Most recently completed are:

  1. Mina Asgari, "A Probabilistic Algorithm for the Solution of Homogeneous Linear Inequalities", MSc. Mathematics.
  2. Pooyan Shirvani Ghomi, On Murty's Gravitational Interior Point method for Quadratic Programming", MSc. Mathematics. Pooyan will start a PhD program at the University of Calgary in September 2010.
  3. Brendan Eagen, "Analysis of Scheduling in a Diagnostic Imaging Department: A Simulation Study", MASc. Industrial and Manufacturing Systems Engineering, Co-supervised with W. Abdul-Kader. Brendan is now an Industrial Engineering PhD Student at the University of Toronto working with Dr. Michael Carter.
  4. Vera Vasilyeva, "An analysis of Murty’s proposed interior point method for quadratic programming", MSc. (Thesis), 2008, now completing graduate work in financial mathematics at the University of Western Ontario.
  5. Adam Hartfiel, “Extreme point detection and the polar dual”, MSc. (Thesis), Mathematics, 2007. Adam is now in a Computer Science PhD program at Waterloo.
  6. Kevin Durda, “Investigating the Structure of Semantic Memory”, 2006. MSc. (Thesis) Mathematics co-supervised with Dr. Lori Buchanan (Psychology). Kevin is now in a doctoral program in Computer Science at Windsor.