Research

• Interior-Point Methods for Nonlinear, Second-Order Cone and Semidefinite Programming

• SIOPT-08 (with A. Sen and D.F. Shanno) "Convergence Analysis of an Interior-Point Method for Nonconvex Nonlinear Programming" In preparation for submission to the SIAM Journal on Optimization, July 2008
• OMS-07 "Mixed-Integer Nonlinear Programming Using Interior-Point Methods" Submitted to Optimization Methods and Software, November 2007
• ACC-08 (with P. Abichandani and M. Kam) "Multi-Vehicle Path Coordination under Communication Constraints" To appear in the Proceedings of the American Control Conference, 2008.
• AOR-08 (with I. Griva, D.F. Shanno, R.J. Vanderbei) "Global Convergence of a Primal-Dual Interior-Point Method for Nonlinear Programming" To appear in Algorithmic Operations Research
• COAP-08 (with D.F. Shanno) "Interior-Point Methods for Nonconvex Nonlinear Programming: Regularization and Warmstarts" Computational Optimization and Applications 40(2), 143-189, June 2008.
• COAP-07 (with D.F. Shanno) "An Exact Primal-Dual Penalty Method Approach to Warmstarting Interior-Point Methods for Linear Programming" Computational Optimization and Applications 38(3), 371-399, December 2007.
• COAP-06 (with A. Sen, D.F. Shanno, and R.J. Vanderbei) "Interior-Point Algorithms, Penalty Methods, and Equilibrium Constraints" Computational Optimization and Applications 34(2), 155-182, June 2006.
• NEDSI-06 (with W. Hu and X. Liu) "Nonlinear Programming for Supply Chain Management: A Survey and Extensions" Proceedings of the Northeast Decision Sciences Institute, Puerto Rico, USA 2006.
• NEDSI-05 "Optimal pricing and procurement strategies in a supply chain with multiple capacitated suppliers" Proceedings of the Northeast Decision Sciences Institute Meeting, Philadelphia, USA, 2005.
• AIMS-04 (with A. Banerjee) "Lot Sizing for Group Technology Cells: A Mixed Integer Nonlinear Model with Complementarity Constraints" Proceedings of the Second AIMS International Conference on Management, 2004
• MathProg-04 (with R.J. Vanderbei and D.F. Shanno) ``Interior-Point Methods for Nonconvex Nonlinear Programming: Jamming and Comparative Numerical Testing'' Mathematical Programming Series A 99(1), 35-48, January 2004.
• Erice-03 (with D.F. Shanno and R.J. Vanderbei) ``A Comparative Study of Large Scale Nonlinear Optimization Algorithms'' In High Performance Algorithms and Software for Nonlinear Optimization, G. Di Pillo and A. Murli, editors, pages 94-126, Kluwer Academic Publishers, 2003.
• Seventh DIMACS Challenge. (with R.J. Vanderbei) ``Solving Problems with Semidefinite and Related Constraints Using Interior-Point Methods for Nonlinear Programming'' Math Programming B, 95(2), 279-302, February 2003.
• GHGT-6. (with J.M. Ogden) "Mathematical Programming Techniques for Designing Minimum Cost Pipeline Networks for CO2 Sequestration" Proceedings of the Sixth Green House Gas Technologies Conference, Kyoto, Japan, 2002.
• COAP-02. (with D.F. Shanno and R.J. Vanderbei) ``Interior-Point Methods for Nonconvex Nonlinear Programming: Filter Methods and Merit Functions'' Computational Optimization and Applications, 23(2): 257-272, November 2002.
• ORFE 02-02. (with D.F. Shanno and R.J. Vanderbei) ``Interior-Point Methods for Nonconvex Nonlinear Programming: Complementarity Constraints''
• ORFE 99-01. (with R.J. Vanderbei) ``On Formulating Semidefinite Programming Problems as Smooth Convex Nonlinear Optimization Problems''
• SOR 98-09. (with R.J. Vanderbei) ``Using LOQO to Solve Second-Order Cone Programming Problems''

I have been working on creating a library of test problems written in AMPL.

• CUTE models converted from SIF
• Schittkowski suite

I have been working with and making enhancements to Dr. Robert J. Vanderbei's interior-point method code for nonconvex nonlinear programming, LOQO.