Research Topics

• Semidefinite programming methods for discrete optimization problems
• Applications of robust optimization techniques
• Convex programming based approximation algorithms for network flows and related problems
• Mechanism design
• Approximately optimal control policies for queueing networks
• Revenue Management
• Growth optimal investment problems
• Applications in signal processing and communication
• Odds and ends

Semidefinite programming methods for discrete optimization problems

• Semidefinite relaxations for the traveling salesman problem
  • with Mehmet T. Cezik
  • CORC Technical Report TR-2001-01
• Cutting planes for mixed 0-1 semidefinite programming
  • with Mehmet T. Cezik
  • CORC Technical Report TR-2001-03
  • Preliminary version appeared in Proceedings of IPCO VIII (2002).
  • Math. Programming, 104(1), pp. 179-202, 2005.    
• Convex quadratic cuts for mixed 0-1 quadratic programming
  • with Mehmet T. Cezik
  • CORC Technical Report TR-2001-02

Applications of robust optimization techniques

• Robust portfolio selection problems
  • with D. Goldfarb
  • Math. Oper. Res., 28(1), pp.1-37, 2003.
  • CORC Technical Report TR-2002-03
• Robust portfolio management 
  • with D. Goldfarb and E. Erdogan
  • Under review in Computational Finance.
  • CORC Technical Report TR-2004-11
• Robust quadratically constrained programs
  • with D. Goldfarb
  • Math. Programming, Ser. B, 97(3), pp.495-515, 2003
  • CORC Technical Report TR-2002-04
• Robust dynamic programming
  • Math. Oper. Res., 30(2), pp.1-21, 2005.
  • CORC Technical Report TR-2002-07
• Inverse conic optimization
  • with Wanmo Kang
  • Oper. Res. Letters, 33(3), pp.319-330, 2005.
  • CORC Technical Report TR-2003-02
• An active set method for single-cone second-order cone programs
  • with Emre Erdogan
  • SIOPT, 17(2) , pp. 459-484, 2006.
  • CORC Technical Report TR-2004-07
• Ambiguous chance constrained problems and robust optimization
  • with Emre Erdogan
  •  Math. Prog., Ser. B 107(1-2), pp. 37-61, 2006.
  • CORC Technical Report TR-2004-10
• On two-stage convex chance constrained problems
• with Emre Erdogan
• To appear in Math. Methods of Oper. Res.
• CORC Technical Report TR-2005-02
• Robust pension fund management
• with Alfred Ma
• CORC Technical Report TR-2006-05

Convex programming based approximation algorithms for network flows and related problems

• Concurrent flows in O(1/epsilon) time
  • with Dan Bienstock
  • Appeared in Proceedings of STOC 2004
  • CORC Technical Report TR-2003-03
• Approximation algorithms for semidefinite packing problems with applications to MAXCUT and graph coloring
  • with David Phillips and Cliff Stein
  • Appeared in Proceedings of IPCO XI (2005)
  • CORC Technical Report TR-2004-06
• Faster approximation for packing and covering problems 
  • with Dan Bienstock
  • SIAM J. Computing, 35(4) , pp. 825-854, 2006.
  • CORC Technical Report TR-2004-09

Mechanism design for supply chains

• Optimal Procurement Auctions for Divisible Goods with Capacitated Suppliers 
• with Anuj Kumar
• under review in Review of Economic Design
• CORC Technical Report TR-2006-01
• Characterizing optimal adword auctions
• with Anuj Kumar
• under review in Operations Research
• CORC Technical Report TR-2006-04 (http://arxiv.org/abs/cs.GT/0611063)
• An equilibrium model for matching impatient demand with patient supply over time
• with Anuj Kumar
• To appear in the Proceeding of EC 2007
• http://aps.arxiv.org/abs/cs.GT/0612065

Revenue management

• Managing correlated callable products on a network
• with Guillermo Gallego
• CORC Technical Report TR-2005-05
• Managing flexible products on a network
  • with A. Dubey, G. Gallego and R. Phillips
  • Under second review in Operations Research
  • CORC Technical Report TR-2004-01

Approximately optimal control policies for queuing networks

• Exponential penalty function based control policies for loss queues
• with K. Sigman
• Ann. Appl. Prob. 14(4), pp.1698-1740, 2004.
• CORC Technical Report TR-2003-04

Growth optimal investment

• Growth optimal investment in horse race markets with costs
• with T. Cover
• IEEE Trans. Info. Theory, 46(7), pp. 2675-1683, 2000
• Discrete time growth optimal investment with proportional transaction cost
  • PDF
• Universal investment in markets with transaction costs
  • Math. Finance, 15(2), pp. 359-371, 2005.
    
  • PDF
• Continuous time growth optimal investment with proportional transaction costs
  • Technical Report # 98, Department of Statistics, Stanford University

Applications in signal processing and communication

• A new method of channel shortening with applications to discrete multi-tone (DMT) systems, Part I : Theory
• with D. Pal and J. M. Cioffi
• Preliminary version in the Proceeding of IEEE International Conference on Communication (ICC) 1998
• ps.gz
• A new method of channel shortening with applications to discrete multi-tone (DMT) systems, Part II: Training
  • with D. Pal and J. M. Cioffi
  • ps.gz

Odds and ends

• A note on martingale on trees: a mathematical programming approach for pricing options
• Technical Report # 90, Department of Statistics, Stanford University
• PDF
• An optimal Riemannian metric for pattern classification
  • with A. Agashe and N. Karmarkar
  • Unpublished manuscript