Faculty Directory

 

Dr. Tits' main research interests lie in various aspects of optimization, with emphasis on numerical methods for convex and nonconvex optimization. In addition to carrying out fundamental research work in these areas, researchers in Dr. Tits' group have developed several software packages. Especially popular is FSQP, a tandem of sophisticated software suites for nonlinear constrainted optimization, in use at over 1000 sites around the world.   

Optimization

1. J. L. Zhou and A. L. Tits, An SQP Algorithm for Finely Discretized Continuous Minimax Problems and Other Minimax Problems With Many Objective Functions, SIAM Journal on Optimization, Vol. 6, No. 2, 1996, pp. 461-487. PDF file. Also see Erratum, SIAM Journal on Optimization, Vol. 8, No. 1, 1998: PDF file
2. C. T. Lawrence and A. L. Tits, Feasible Sequential Quadratic Programming for Finely Discretized Problems from SIP, In R. Reemtsen, J.-J. Ruckmann (eds.): Semi-Infinite Programming, in the series Nonconvex Optimization and its Applications. Kluwer Academic Publishers, 1998, pp. 159-193. PDF file. Also see Erratum: PDF file
3. C.T. Lawrence and A.L. Tits, A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm, SIAM J. Optimization, Vol. 11, No. 4, 2001, pp. 1092-1118. PDF file.
4. A.L. Tits, A. Waechter, S. Bakhtiari, T.J. Urban and C.T. Lawrence, A Primal-Dual Interior-Point Method for Nonlinear Programming with Strong Global and Local Convergence Properties, SIAM J. Optimization, Vol. 14, No. 1, pp. 173-199, 2003. PDF file.
5. S. Bakhtiari and A.L. Tits, A Simple Primal-Dual Feasible Interior-Point Method for Nonlinear Programming with Monotone Descent, Computational Optimization and Applications, Vol. 25, pp. 17-38, 2003. PDF file
6. A.L. Tits, P.A. Absil and W.P. Woessner, Constraint Reduction for Linear Programs with Many Inequality Constraints, SIAM J. Optimization, Vol. 17, No. 1, pp. 119-146, 2006. PDF file.
7. S. Schurr, A.L. Tits and D. O'Leary, Universal Duality in Conic Convex Optimization, Mathematical Programming, Series A, Vol. 109, No. 1, pp. 69-88, 2007. PDF file.
8. P.A. Absil and A.L. Tits, Newton-KKT Interior-Point Methods for Indefinite Quadratic Programming, Computational Optimization and Applications, Vol. 36, pp. 5-41, 2007. PDF file.
9. C.D. Hauck, C.D. Levermore and A.L. Tits, Convex Duality and Entropy-Based Moment Closures: Characterizing Degenerate Densities, SIAM J. Control Optim., Vol. 47, No. 4, pp. 1977-2015, 2008.
10. J.H. Jung, D.P. O'Leary, and A.L. Tits, Adaptive Constraint Reduction for Training Support Vector Machines, Electronic Transactions on Numerical Analysis, Vol. 31, pp. 156-177, 2008. PDF file.
11. S.P. Schurr, D.P. O'Leary, and A.L. Tits, A polynomial-time interior-point method for conic optimization, with inexact barrier evaluations, SIAM J. Optimization, Vol. 20, No. 1, pp. 548-571, 2009. PDF file. PDF file.
12. L.B. Winternitz, S.O. Nicholls, A.L. Tits and D.P. O'Leary, A Constraint-Reduced Variant of Mehrotra's Predictor-Corrector Algorithm, Computational Optimization and Applications, Vol. 51, No. 1, pp. 1001-1036, 2012. PDF file.
13. J.H. Jung, D.P. O'Leary, and A.L. Tits, Adaptive Constraint Reduction for Convex Quadratic Programming, Computational Optimization and Applications, Vol. 51, No. 1, pp. 125-157, 2012. PDF file.
14. M.Y. He and A.L. Tits, Infeasible constraint-reduced interior-point methods for linear optimization, Optimization Methods and Software, Vol. 27, No. 4-5, pp. 801-825, 2012. PDF file.
15. G.W. Alldredge, C.D. Hauck, and A.L. Tits, High-order, entropy-based closures for linear transport in slab geometry II: A computational study of the optimization problem, SIAM J. on Scientific Computation, 34(4), B361-B391, 2012. PDF file.
16. L.B. Winternitz, A.L. Tits, and P.-A. Absil, Addressing rank degeneracy in constraint-reduced interior-point methods for linear optimization, Journal of Optimization, Theory and Applications, 2013. PDF file.
17. G.W. Alldredge, C.D. Hauck, D.P. O'Leary, and A.L. Tits, Adaptive change of basis in entropy-based moment closures for linear kinetic equations, Journal of Computational Physics, Vol. 258, pp.~489--508, 2014. PDF file.
18. M.P. Laiu, C.D. Hauck, R.G. McClarren, D.P. O'Leary, and A.L. Tits, Positive Filtered PN Moment Closure for Linear Kinetic Transport Equations, SIAM J. Numerical Analysis, Vol. 54-6, 2016, pp. 3214--3238.
19. M.P. Laiu and A.L. Tits, A Constraint-Reduced MPC Algorithm for Convex Quadratic Programming, with a Modified Active Set Identification Scheme, to appear in Computational Optimization and Applications, 2019. PDF file.

Control Theory

1. A.L. Tits, V. Balakrishnan and L. Lee, Robustness under Bounded Uncertainty with Phase Information, IEEE Trans. on Automatic Control, vol. 44, no. 1, 1999. PDF file
2. A.L. Tits and V. Balakrishnan, Small-mu Theorems with Frequency-Dependent Uncertainty Bounds, Math. of Control, Signals and Sytems, vol. 11, pp. 220-243, 1998. PDf file
3. Y.S. Chou, A.L. Tits and V. Balakrishnan, Absolute Stability Theory, $\mu$ Theory, and State-Space Verification of Frequency-Domain Conditions: Connections and Implications for Computation, IEEE Trans. on Automatic Control, vol. 44, No. 5, May 1999, pp. 906-913. PDF file
4. C.T. Lawrence, A.L. Tits and P. Van Dooren, A Fast Algorithm for the Computation of an Upper Bound on the Mu-Norm, Automatica, Vol. 36, No. 3, 2000, pp. 449-456. PDF file
5. A.A. Kale and A.L. Tits, On Kharitonov's Theorem Without Invariant Degree Assumption, Automatica, vol. 36, No. 7, 2000, pp. 1075-1076. PDF file
6. A.L. Tits and Y.-S. Chou, On Mixed-Mu Synthesis, Automatica, vol. 36, No. 7, 2000, pp. 1077-1079. PDF file
7. V. Sima, A.L. Tits, and Y. Yang, Computational experience with robust pole assignment algorithms, Proceedings of the 2006 IEEE International Conference on Control Applications (CCA), 2006 IEEE Conference on Computer-Aided Control Systems Design (CACSD) 2006 IEEE International Symposium on Intelligent Control (ISIC), Technische Universität München, Munich, Germany, October 4-6, 2006, pp.36-41, Omnipress. PDF file