Reha Tütüncü

Associate Professor
Ph.D., Cornell University

Office: Wean Hall 7219
Phone: (412) 268-2558
E-mail: reha@andrew.cmu.edu
Personal web site

Research

My research interests lie in optimization theory and application of optimization techniques to problems in arising in financial and engineering models. On the theory side, I work on the development, analysis, and implementation of interior-point methods for the solution of convex optimization problems. In particular, I studied potential-reduction methods for linear optimization problems and have been collaborating with Mike Todd and Kim Toh on development of algorithms and software for semidefinite programming and second-order cone programming problems. SDPT3 is the product of this collaboration.

My work on the application of optimization techniques focuses on financial and chemical engineering problems. In recent projects, I studied a new method for fast and reliable computation of the optimal risky portfolios and worked on the development of a new algorithm for robust solution of asset allocation problems when the statistical input parameters are unreliable. Current projects include multivariate model fitting problems and risk management using coherent risk measures.

Selected Publications

E. J. Chester and R. H. Tütüncü. "Rendezvous search on finite domains." June 2001. Submitted.

R. H. Tütüncü, K. C. Toh, and M. J. Todd. "Solving semidefinite-quadratic-linear programs using SDPT3." March 2001. Submitted to Mathematical Programming.

R. H. Tütüncü. "A note on calculating the optimal risky portfolio," Finance and Stochastics, Vol. 5, No. 3, pp. 413–417 (2001).

B. V. Halldórsson and R. H. Tütüncü. "An interior-point method for a class of saddle point problems," Current version: April 2000. Submitted to Journal of Optimization Theory and Applications.

A. M. Cervantes, A. Wächter, R. H. Tütüncü, and L. Biegler. "A reduced space interior point strategy for optimization of differential algebraic systems," Computers and Chemical Engineering, Vol. 24, No. 1, pp. 39–51 (2000).

R. H. Tütüncü. "Quadratic convergence of potential-reduction methods for degenerate problems," Mathematical Programming, Vol. 90, No. 1, pp. 169–203 (2001).

R. H. Tütüncü. "A primal-dual variant of the Iri-Imai algorithm for linear programming," Mathematics of Operations Research, Vol. 25, No. 2, pp. 195–213 (2000).

K. C. Toh, M. J. Todd, and R. H. Tütüncü. "SDPT3 — a Matlab software package for semidefinite programming," Optimization Methods and Software, Vol. 11/12, pp. 545–581 (1999).

R. H. Tütüncü. "An Infeasible-Interior-Point Potential-Reduction Method For Linear Programming," Mathematical Programming, Vol. 86, No. 2, pp. 313–334 (1999).

M. J. Todd, K. C. Toh, and R. H. Tütüncü. "On the Nesterov-Todd Direction in Semidefinite Programming," SIAM J. on Optimization, Vol. 8, No. 3, pp. 769–796 (1998).

Course Web sites

21-690: Methods of Optimization

21-365: Projects in Applied Mathematics

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