Kurt M. Anstreicher

Tippie Research Professor of Management Sciences
S322 Pappajohn Building
The University of Iowa
Iowa City, IA 52242-1000
kurt-anstreicher@uiowa.edu

Academic History:

Appointment at Iowa: 1991

Research Interests:

My research is in the area of optimization and mathematical programming. I am especially interested in interior point methods for linear, nonlinear, and semidefinite programming, and in the application of continuous nonlinear relaxations to obtain bounds on integer nonlinear programming problems.

Selected Publications

• "On Partial Updating in a Potential Reduction Linear Programming Algorithm of Kojima, Mizuno, and Yoshise" (with R.A. Bosch), Algorithmica 9 (1993), 184-197.
• "A Family of Search Directions for Karmarkar's Algorithm" (with P. Watteyne), Operations Research 41 (1993), 759-767.
• "A Long-Step Barrier Method for Convex Quadratic Programming" (with D. den Hertog, C. Roos, and T. Terlaky), Algorithmica , 10 (1993), 365-382.
• "Strict Monotonicity and Improved Complexity in the Standard Form Projective Algorithm for Linear Programming," Mathematical Programming 62 (1993), 517-535.
• "On Quadratic and $O(\sqrt{n}L)$ Convergence of a Predictor-Corrector Algorithm for LCP" (with Y. Ye), Mathematical Programming 62 (1993), 537-551.
• "A Monotonic Build-Up Simplex Algorithm for Linear Programming" (with T. Terlaky), Operations Research 42 (1994), 556-561.
• "On the Convergence of an Infeasible Primal-Dual Interior-Point Method for Convex Programming" (with J.-P. Vial), Optimization Methods and Software 3 (1994), 273-283.
• "A New Infinity-Norm Path Following Algorithm for Linear Programming" (with R.A. Bosch), SIAM Journal on Optimization 5 (1994), 236-246.
• "A Partial Updating Algorithm for Linear Programs with Many More Variables than Constraints" (with R.A. Bosch), Optimization Methods and Software 4 (1995), 243-257.
• "On Long Step Path Following and SUMT for Linear and Quadratic Programming," SIAM Journal on Optimization 6 (1996), 33-46.
• "Large Step Volumetric Potential Reduction Algorithms for Linear Programming," Annals of Operations Research 62 (1996), 521-538.
• "Volumetric Path Following Algorithms for Linear Programming," Mathematical Programming 76 (1997), 245-263.
• "On Vaidya's Volumetric Cutting Plane Method for Convex Programming," Mathematics of Operations Research 22 (1997), 63-89.
• "A Long-Step Path Following Algorithm for Semidefinite Programming Problems" (with M. Fampa), in Topics in Semidefinite and Interior-Point Methods , P.M. Pardalos and H. Wolkowicz, eds., The Fields Institute for Research in Mathematical Sciences Communications Series , American Mathematical Society, Providence, R.I. (1998), 181-196.
• Towards a Practical Volumetric Cutting Plane Method for Convex Programming, SIAM Journal on Optimization 9 (1999), 190-206.
• "Probabilistic Analysis of an Infeasible-Interior-Point Algorithm for Linear Programming" (with J. Ji, F.A. Potra, and Y. Ye), Mathematics of Operations Research 24 (1999), 176-192.
• "Ellipsoidal Approximations of Convex Sets Based on the Volumetric Barrier," Mathematics of Operations Research 24 (1999), 193-203.
• Using Continuous Nonlinear Relaxations to Solve Constrained Maximum--Entropy Sampling Problems (with M. Fampa, J. Lee, and J. Williams), Mathematical Programming 85 (1999), 221-240.
• Linear Programming in O([n^3/ln n]L) Operations, SIAM Journal on Optimization 9 (1999), 803-812.
• "Strong Duality for a Trust-Region Type Relaxation of the Quadratic Assignment Problem" (with X. Chen, H. Wolkowicz, and Y. Yuan), Linear Algebra and its Applications 301 (1999), 121-136.
• "The Volumetric Barrier for Semidefinite Programming," Mathematics of Operations Research 25 (2000), 365-380. [volume6.ps]
• On Lagrangian Relaxation of Quadratic Matrix Constraints (with H. Wolkowicz), SIAM Journal on Matrix Analysis and Application 22 (2000), 41-55.
• Maximum-Entropy Remote Sampling (with M. Fampa, J. Lee, and J. Williams), Discrete Applied Mathematics 108 (2001), 259-274.
• A Note on the Augmented Hessian When the Reduced Hessian is Semidefinite (with M.H. Wright), SIAM Journal on Optimization 11 (2001), 243-253.
• Eigenvalue Bounds Versus Semidefinite Relaxations for the Quadratic Assignment Problem, SIAM Journal on Optimization 11 (2001), 254-265.
• A New Bound for the Quadratic Assignment Problem Based on Convex Quadratic Programming (with N.W. Brixius), Mathematical Programming 89 (2001), 341-357.
• "Solving Quadratic Assignment Problems Using Convex Quadratic Programming Relaxations" (with N.W. Brixius), Optimization Methods and Software 16 (2001), 49-68. [qapqp2.ps]
• Solving Large Quadratic Assignment Problems on Computational Grids (with N. Brixius, J. Linderoth, and J.-P. Goux), Mathematical Programming, Series B 91 (2002), 563-588. Winner, SIAM Activity Group on Optimization (SIAG/OPT) Prize, May 2002.
• Improved Linear Programming Bounds for Antipodal Spherical Codes Discrete and Computational Geometry 28 (2002), 107-114.

Recent Working Papers

The following are available in .ps or .pdf format.

• "On the Equivalence of Convex Programming Bounds for Boolean Quadratic Programming," May 1998. [bqp.ps]
• "The Volumetric Barrier for Convex Quadratic Constraints," to appear in Mathematical Programming. [volume7.ps]
• "A Pentomino Exclusion Problem," February 1999. [pento.ps]
• "Improved Complexity for Maximum Volume Inscribed Ellipsoids," to appear in SIAM Journal on Optimization. [mvie.ps]
• "The Steinberg Wiring Problem" (with N.W. Brixius), to appear in The Sharpest Cut, Festschrift in Honor of Manfred Padberg's 60th Birthday, M. Groetschel, editor, SIAM, 2003. [wiring.ps] Slides for talk
• "The Thirteen Spheres: A New Proof," to appear in Discrete and Computational Geometry. [thirteen.pdf] Slides for talk
• "D.C. Versus Copositive Bounds for Standard QP" (with S. Burer), May 2003, revised January 2004. [dcqp2.ps]
• "A Masked Spectral Bound for Maximum-Entropy Sampling" (with J. Lee), September 2003. [mask.pdf]