Dr. Warren Hare received his Ph.D. in Mathematical Optimization from Simon Fraser University. Following this he has been a postdoctoral fellow at IMPA - Brazil and at McMaster University before returning to SFU to become the Program Director for the MoCSSy Program. He is currently an Assistant Professor at UBC, Okanagan Campus. His research focuses on Understanding and Exploiting Sub-structure in Optimization Problem..
Research Interest: Understanding and Exploiting Substructure in Optimization Problems.
Optimization, the study of minimizing of maximizing a function, arises naturally in almost every scientific research field. Applications can be found in everything from business (e.g., minimizing cost and maximizing profit), to engineering (e.g., maximizing structural integrity and minimizing hospital wait times), to theoretical mathematics (e.g., explaining the continuity of minimizers of proximal averages and understanding stability of prox-regular functions).
In many optimization problems, a close examination of the problem will reveal substructures that can used to help understand and solve the problem. One classic example is Linear Programming, where understanding of the very strong substructure allowed for the development of the powerful Simplex Method. In my research, I explore more subtle examples of substructure that arise in optimization.
I view my research as having three major branches: Applied Optimization, Algorithm Design, and Mathematical Theory. In Applied Optimization we work with real-world problems (usually provided by an industrial partner) and research methods to model and solve the problems. By understanding a problem's model we can often determine and exploit substructure within the problem to greatly improve solution times and quality. In Algorithm Design, develop new methods of solving optimization problems, both by proving theoretical convergence and implementing them as computer software. Many of these methods are designed to work for black-box problems with specific substructure, and demonstrated to have greatly improve convergence when used on such problems. In Mathematical Theory we research concepts from functional and variational analysis. These ideas help us understand ideas like generalized convexity and active manifolds.
Selected Publications and Preprints:
Please feel free to contact me regarding any paper or report you cannot find at your local library
For a full list of publications and research reports please visit my Research Gate profile.
- Complex Systems Modelling Group (15 members, principal authors: W. Hare, A. Rutherford, & K. Vasarhelyi). ``Modelling in Healthcare.'' American Mathematical Society, Providence, USA, pp. xviii+212 (2010). [AMS bookstore]
- W. L. Hare, V. R. Koch, & Y. Lucet. "Improving earthwork operations for road design via mixed integer linear programming." European Journal of Operations Research, 215(2), pp 470--480 (2011). [science direct]
- K. Bigdeli, W. Hare, \& S. Tesfamariam. "Configuration optimization of dampers for adjacent buildings under seismic excitations." Engineering Optimization, 44(12) (2012). [T&F online]
- W. Hare & J. Nutini. "A derivative-free approximate gradient sampling algorithm for finite minimax problems" Computational Optimization and Applications", to appear (2013). [springer online]
- W. Hare & C. Sagastizabal “Redistributed Proximal Bundle Method for Nonconvex Optimization.” SIAM J. Opt., 20(5), pp 2442--2473 (2010). [springer online]
- W. L. Hare & C. Sagastizabal. “Computing Proximal Points of Nonconvex Functions.” Mathematical Programming series B, 116, pp 221–258 (2009). [springer online]
Mathematics of Substructure in Optimization
- C. Davis & W. Hare. "Exploiting Known Structures to Approximate Normal Cones." Mathematics of Operations Research, to appear, (2013). [INFORMS]
- R. Goebel, W. Hare, & X. Wang. "The Optimal Value and Optimal Solutions of The Proximal Average of Convex Functions." Nonlinear Analysis: Theory, Methods, Applications, 75(3), pp 1290--1304 (2012). [science direct]
- W. L. Hare. “The Proximal Average of Nonconvex Functions: A Proximal Point Perspective.” SIAM Journal on Optimization, 20(2), pp 650-666 (2009) . [springer online]
- W. L. Hare & R. A. Poliquin. “Prox-Regularity and Stability of the Proximal Mapping.” Journal of Convex Analysis, 14, No. 3, pp 589–606 (2007). [JCA online]
Last reviewed 3/4/2013 11:01:47 AM