Publications

1. "Operational Axiomatic Accounting Mechanics," Accounting Review XLI, (3), 1966, 426-442.
2. "Nonlinear Programming Via Kakutani Fixed Points," Working Paper No. 294, Center for Research in Management Science, University of California, Berkeley, February 1970.
3. "An Odd Theorem," Proceedings of American Mathematical Society 26, (3), 1970, 509- 513.
4. "The Linear Complementarity Problem," Management Science 17, (9), 1971, 612- 634.
5. "On Quadratic Programming," Management Science 7, (11), 1971, 698- 711.
6. "Computing Kakutani Fixed Points," SIAM Journal on Applied Mathematics 21, (2), 1971, 236-244.
7. . "On the Basic Theorem of Complementarity," Mathematical Programming 1, (1), 1971, 68-75.
8. "Generalized Cutting Plane Algorithms," co-authored with W.I. Zangwill, SIAM Journal on Control 9, (4), 1971, 529-542.
9. "Homotopies for Computation of Fixed Points," Mathematical Programming 3, (1), 1972, 1- 22.
10. "Homotopies for Computation of Fixed Points on Unbounded Regions," co- authored with R. Saigal, Mathematical Programming 3, (2), 1972, 225-237.
11. "Polymatrix Games with Joint Constraints," SIAM Journal on Applied Mathematics 24, (3), 1973, 418-423 .
12. "Fourier-Motzkin Elimination and Its Dual," with G.B. Dantzig, Journal of Combinatorial Theory 14, (3), 1973, 288-297.
13. "Piecewise Linear Retractions by Reflection," Linear Algebra and Its Applications 7, 1973, 93-98.
14. "On the Need of a System Optimization Laboratory," with G.B. Dantzig, R.W. Cottle, F.S. Hillier, A.S. Manne, G.H. Golub, D.J. Wilde, R.B. Wilson, Mathematical Programming, (ed.: T.C. Hu and S.M. Robinson), Academic Press, 1973, 1-32.
15. "Properly Labeled Simplexes," Studies in Optimization 10, MAA Studies in Mathematics, (ed.: with G.B. Dantzig), 1974, 71-93.
16. "Solving Piecewise Linear Convex Equations," Mathematical Programming Study 1, dedicated to A.W. Tucker, 1974, 96-119.
17. "Studies in Optimization," (ed. with G.B. Dantzig), MAA Studies in Mathematics 10, 1974.
18. "The Solution of Systems of Piecewise Linear Equations," with H. Scarf, Mathematics of Operations Research 1, (1), 1976, 1-27.
19. "A Finite Algorithm for the Linear Exchange Model," Journal of Mathematical Economics 3, 1976, 197-203.
20. "A Short Course in Solving Equations with PL Homotopies," SIAM-AMS Proceedings IX, 1976, 73-143.
21. "Complementary Pivot Theory and Markovian Decision Chains," in Fixed Points: Algorithms and Applications, (ed. Stepan Karamardian), Academic Press, Inc., New York, 1977, 59- 85.
22. "A Finite Procedure for Determining if A Quadratic Form is Bounded Below on a Polyhedral Convex Set," Mathematical Programming 14, 1978, 122-124.
23. "Computing Stationary Points," Mathematical Programming Study 7, 1978, 1-14.
24. "Computing Stationary Points, Again," Nonlinear Programming 3, (eds.: Olvi L. Mangasarian, Robert R. Meyer and Stephen M. Robinson), Academic Press, New York, 1978, 391-405.
25. "A Locally Quadratically Convergent Algorithm for Computing Stationary Points," Department of Operations Research, Stanford University, May 1978. See No. 32 for revision, (SOL 78- 13).
26. "An Algorithm for a Piecewise Linear Model of Trade and Production with Negative Prices and Bankruptcy," with G.B. Dantzig and D. Gale, Mathematical Programming 16, 1979, 120- 209.
27. "Computing Economic Equilibria on Affine Networks with Lemke's Algorithm," with R. Asmuth and E. Peterson, Mathematics of Operations Research 4, (3), 1979, 209-214.
28. "A View of Complementary Pivot Theory (or Solving Equations with Homotopies)," Functional Differential Equations and Approximation of Fixed Points, (eds.: Heinz-Otto Peitgen and Hans-Otto Walther), Springer-Verlag, New York, 1979. Constructive Approaches to Mathematical Models, (eds.: Coffman and Fix), Academic Press, 1979.
29. "Inscribing and Circumscribing Convex Polyhedra," with R.M. Freund, Operations Research Department, Stanford University, March 1979. (Revised as "Optimal Scaling of Balls and Polyhedra," See No. 31.)
30. "Equivalence of LCP and PLS: Part I," with C.E. Lemke, Mathematics of Operations Research 6, (4), 1981, 475-484.
31. "Optimal Scaling of Balls and Polyhedra," with R.M. Freund, Mathematical Programming 23, 1982, 138-147.
32. "Where Solving for Stationary Points by LCP's is Mixing Newton Iterates," Homotopy Methods and Global Convergence 13, (eds.: B.C. Eaves, F.J. Gould, H-O. Peitgen and M.J. Todd), Plenum Press, New York, 1983.
33. "Equivalence of LCP and PLS: Part II," with C.E. Lemke, Homotopy Methods and Global Convergence 13, (eds.: B.C. Eaves, F.J. Gould, H-O. Peitgen and M.J. Todd), Plenum Press, NY, 1983.
34. "Subdivisions from Primal and Dual Cones and Polytopes," Linear Algebra and Its Applications 62 1984, 277-285, (SOL 83-11).
35. "A Course in Triangulations for Solving Equations with Deformations," Lecture Notes in Economics and Mathematical Systems 234, Springer-Verlag, 1984.
36. "Permutation Congruent Transformations of the Freudenthal Triangulation with Minimal Surface Density," Mathematical Programming 29, (1), 1984, 77-99.
37. "Equivalence of Surface Density and Average Directional Density," with J. Yorke, Mathematics of Operations Research 9, (3), 1984, 363-375.
38. "Finite Solution of Pure Trade Markets with Cobb-Douglas Utilities," Mathematical Programming Study 23, 1985, 226-239.
39. "A Decomposition and Scaling-Inequality for Line-Sum-Symmetric Nonnegative Matrices," with G.B. Dantzig and Uriel G. Rothblum, SIAM Journal on Algebraic and Discrete Methods 6, (2), 1985, 237-241.
40. "Line-Sum-Symmetric Scalings of Square Nonnegative Matrices," with A.J. Hoffman, Uriel G. Rothblum and Hans Schneider, Mathematical Programming Study 25, (2), 1985, 124-141.
41. "A Variable Rate Refining Triangulation," with Mark N. Broadie, Mathematical Programming 38, 1987, 161-202.
42. "Thoughts of Computing Market Equilibrium with SLCP," in The Computation and Modeling of Economic Equilibria, (ed.: A.J.J. Talman, G. van der Laan), North-Holland, 1987, 1- 17.
43. "Dines-Fourier-Motzkin Quantifier Elimination and an Application of Corresponding Transfer Principles over Ordered Fields," with Uriel G. Rothblum, Mathematical Programming 53, 1992, 307- 321.
44. "Invariant Polynomial Curves of Piecewise Linear Maps," with Uriel G. Rothblum, SIAM Journal on Control & Optimization 26, (2), 1988, 401-416.
45. "A Discrete Time Average Cost Flexible Manufacturing and Operator Scheduling Model Solved by Deconvexification Over Time," with Uriel G. Rothblum, the Journal of the Operations Research Society of America 36, (2), 1988, 242-257.
46. "A Continuous Time Average Cost Flexible Manufacturing and Operator Scheduling Model Solved by Deconvexification Over Time," with Uriel G. Rothblum, Linear Algebra and Its Applications 114/115, 1989, 417-429.
47. "A Theory on Extending Algorithms for Parametric Problems," with Uriel G. Rothblum, Mathematics of Operations Research 14, 1989, 502-533.
48. "A Class of "Onto" Multifunctions," with Uriel G. Rothblum, Mathematical Programming 61, (3), 1993, 327-343.
49. "Arrangements of Linear Programs with Spheres and Hemispheres of Objective Vectors," Department of Operations Research, Stanford University, August 1989, submitted to Mathematical Programming.
50. "Covers by Polars of Arrangements," with A.J. Hoffman, Department of Operations Research, Stanford University, August 1990, submitted to Linear Algebra and Its Applications.
51. "Relationships of Properties of Piecewise Affine Maps Over Ordered Fields," with Uriel G. Rothblum, Linear Algebra and Its Applications 132, 1990, 1-63.
52. "Deforming Subdivisions," Mathematical Programming 48 (3), 1990, 359- 367.
53. "A Discounted-Cost Continuous-Time Flexible Manufacturing and Operator Scheduling Model Solved by Deconvexification Over Time," with Uriel Rothblum, Probability in the Information and Engineering Sciences 9, 1995, 65-98.
54. "Linear Programming with Spheres and Hemispheres of Objective Vectors," with Alan J. Hoffman, and Hui Hu, Mathematical Programming 51, (1) 1991, 1-16.
55. "Pivoting to Normalize a Matrix," Mathematical Programming 62, (3), 1993, 553- 557.
56. "Formulation of Linear Problems and Solution by a Universal Machine," with Uriel Rothblum, Department of Operations Research, Stanford University, September 1992. Mathematical Programming 65 (3) 1994, 263-309.
57. "Computing Zeros of Sections of Vector Bundles Using Homotopies and Relocalization," with Donald Brown and Peter DeMarzo, Mathematics of Operations Research 21, (1), 1996, 26- 43.
58. "Computing Equilibria in the GEI Model," with Donald Brown and Peter DeMarzo, Econometrica 64, (1), 1996, 1-27.
59. "Complete Solvability of Linear Problems by Randomized Linear Algorithm," with Uriel Rothblum, Department of Operations Research, Stanford University, November 1993.
60. "A Homotopy, Grassmannian Manifold, and Relocalization for Computing Equilibria of GEI," with Peter DeMarzo, Department of Operations Research, Stanford University, August 1993. Submitted to Journal of Mathematical Economics.
61. "Perron-Frobenius Theory Over Real Closed Fields and Fractional Power Series Expansions," with Uriel Rothblum, Linear Algebra and its Applications 220, 1995, 123-150.
62. "Linear Problems and Linear Algorithms," with Uriel G. Rothblum, Journal of Symbolic Computation 11, 1995, 1-8.
63. "Two Courses for Learning the Practice of Operations Research," Education in a Research University (eds.: Kenneth J. Arrow, R.W. Cottle, B. Curtis Eaves, Ingram Olkin), Stanford University Press, Stanford, CA, 1996.
64. Education in a Research University, edited with Kenneth J. Arrow, R.W. Cottle, Ingram Olkin, Stanford University Press, Stanford University, Stanford, CA, 1996.
65. "Balanced Simplices on Polytopes," with Gerard van der Laan, Dolf Talman, and Zaifu Yang, Department of Econometrics and CentER, Tilburg University, The Netherlands, September 1995. To appear in Proceedings of Conference in Honor of Herbert E. Scarf.
66. "Parallel Computation of Approximate Parametric Roots of Parametric Polynomials," with Uriel G. Rothblum, Department of Operations Research, Stanford University, October 1995.
67. Complexity of Computing Algebraic Curves, with Uriel G. Rothblum, Department of Operations Research, Stanford University, October 1995. To appear in A.M.S. Proceedings of Park City Conference.
    Last updated 7/12/96