# David G. Luenberger

### Professor David G. Luenberger

Professor

Management Science and Engineering

#### Office: Terman 410

Fax: 650.723.3039

Email: luen @ stanford.edu

**Articles**

1. Luenberger, David G. (1963), “On Barker Codes of Even Length,” *Proceedings of the IEEE* (January 1963) 230–231.

2. Luenberger, David G. (1964), “Observing the State of a Linear System,” *IEEE Transactions on Military Electronics* (April 1964) 74–80.

3. Luenberger, David G. (1965), “A New Derivation of the Quadratic Loss Control Equation,” *IEEE Transactions on Automatic Control*, AC–10 (April 1965) 202– 203.

4. Luenberger, David G. (1965), “Invertible Solutions to the Operator Equation TA – BT = C,” *Proceedings American Mathematical Society*, 16:5 (December 1965) 1226–1229.

5. Luenberger, David G. (1966), “A Generalized Maximum Principle,” in *Recent Advances on Optimization Techniques*, Lavi and Vogl, eds., New York: John Wiley and Sons, Inc.

6. Luenberger, David G. (1965), “Observers for Multivariable Systems,” *IEEE Transactions on Automatic Control*, AC–11:2 (April 1966) 190–197.

7. Luenberger, David G. and Ulric E. Dennis (1966), “Computational Methods for Resolution of Mass Spectra,” *Analytical Chemistry*, 38:6 (1966) 715–720.

8. Luenberger, David G. (1966), Review of: *Dynamic Programming and Modern Control Theory* by R. Bellman and R. Kalaba, in *American Scientist*,54:4 (December 1966) 482.

9. Meier, L. and Luenberger, David G. (1965), “Approximation of Linear Constant Systems,”Preprints 1966 Joint Automatic Control Conference (1966) 728–734. Also published in *IEEE Transactions on Automatic Control*, AC–12:5 (October 1967) 585–588.

10. Anderson, B.D.O. and Luenberger, David G. (1965), “Design of Multivariable Feedback Systems,” *Proceedings of the IEEE* , 114:3 (March 1967) 395–399.

11. Luenberger, David G. (1967), “A Simple Polynomial Estimator,” *IEEE Transactions on Automatic Control*, AC–12:2 (April 1967) 211–212.

12. Luenberger, David G. (1967), “Canonical Forms for Linear Multivariable Systems,” *IEEE Transactions on Automatic Control*, AC–12:3 (June 1967) 290– 293.

13. Sinnott, J. and Luenberger, David G. (1967), “Solution of Optimal Control Problems by the Method of Conjugate Gradients,” Preprints of the 1967 Joint Automatic Control Conference (1967) 74–77.

14. Luenberger, David G. (1967), Review of: State Space Analysis of Control Systems by K. Ogata, in *IEEE Transactions on Automatic Control*, AC–12 (December 1967) 805.

15. Luenberger, David G. (1968), “Tracking of Goal Seeking Vehicles,” *IEEE Transactions on Automatic Control*, AC–13 (February 1968) 74–77.

16. Luenberger, David G. (1968), “Convex Programming and Duality in Normed Space,” Record of the IEEE Systems Science and Cybernetics Conference (October 1967). Also published in *IEEE Transactions on Systems Science and Cybernetics*, SSC–4 (July 1968) 182–188.

17. Luenberger, David G. (1968), “Quasi–Convex Programming,” *SIAM** Journal on Applied Math*, 16 (September 1968) 1090–1095.

18. P. Wong and Luenberger, David G. (1968), “Reducing the Memory Requirements of Dynamic Programming,” *Operations Research*, 16:6 (1968) 1115–1125.

19. Luenberger, David G. (1969), “A Primal Dual Method for the Computation of Optimal Control,” presented at the 2nd International Conference on Computing Methods in Optimization Problems, San Remo, Italy (September 9–13, 1968). Also in *Computing Methods in Optimization Problems–2*, Zadeh, Neustadt, Balakrishnan, eds., Academic Press, 1969, 223–233.

20. Ratner, R. S. and Luenberger, David G. (1969), “Performance–Adaptive Renewal Policies for Linear Systems,” presented at the 2nd Hawaii International Conference on System Science, Honolulu, Hawaii (January 22–24, 1969). Also in *IEEE Transactions on Automatic Control*, AC–14 (1969) 344–351.

21. Rhodes, I. B. and Luenberger, David G. (1969), “Differential Games with Imperfect State Information,” *IEEE Transactions on Automatic Control*, AC– 14 (February 1969) 29–38.

22. Rhodes, I. B. and Luenberger, David G. (1969), “Stochastic Differential Games with Constrained State Estimators,” in Preprints of the 1969 Joint Automatic Control Conference (1969) 539–544. Also published in *IEEE Transactions on Automatic Control*, AC–14 (October 1969) 476–481.

23. Luenberger, David G. (1969), “Hyperbolic Pairs in the Method of Conjugate Gradients,” *SIAM** Journal on Applied Math*, 17 (1969) 1263–1267.

24. Luenberger, David G. (1969), “The Conjugate Residual Method for Constrained Minimization,” *SIAM** Journal on Numerical Analysis*, 7:3 (September 1970) 390–398.

25. Luenberger, David G. (1970), “Control Problems with Kinks,” in Preprints of the 1970 Joint Automatic Control Conference (1969) 539–544. Also published in *IEEE Transactions on Automatic Control*, AC–15:5 (1970) 570–575.

26. Bryson, A. E. Jr. and Luenberger, David G. (1963), “The Synthesis of Regulator Logic Using State–Variable Concepts,” *Proceedings of the IEEE* , 58:11 (1970) 1803–1811.

27. Luenberger, David G. (1971), “Convergence Rate of a Penalty Function Scheme,” *Journal of Optimization Theory and Applications*, 7:1 (1971) 39–51.

28. Luenberger, David G. (1971), “Cyclic Dynamic Programming: A Procedure for Problems with Fixed Delay,” *Operations Research*, 19:4 (1971) 1101–1110.

29. Luenberger, David G. (1971), “Is Current Engineering Education Relevant to the Fundamental Problems Now Facing Society?,” 1st Place Winner of Essay Contest sponsored by Pacific Southwest Section of ASEE, 1971. (Presented at the Spring Meeting in May 1971.)

30. Luenberger, David G. (1971), “An Introduction to Observers,” *IEEE Transactions on Automatic Control*, AC–16:6 (December 1971) 596–602.

31. Wong, P. J., R. M. Dressler and D. G. Luenberger (1971), “A Combined Parallel–Tangents/Penalty Function Approach to Solving Trajectory– Optimization Problems,” *AIAA Journal*, 9:12 (December 1971) 2443–2448.

32. Oren, S. and Luenberger, David G. (1972), “The Self-Scaling Variable Metric Algorithm,” Proceedings of the 5th Hawaii International Conference on Systems Sciences, (January 1972) 130–132.

33. Luenberger, David G. (1972), “Mathematical Programming and Control Theory: Trends of Interplay,” Presented at the 7 th International Symposium on Mathematical Programming, The Hague, The Netherlands (September 1970). Reprinted as Chapter 4 in *Perspectives on Optimization*, A. M. Geoffrion, ed., Reading, Massachusetts: Addison–Wesley, 1972.

34. Jolissaint, C. H., N. V. Arvanitidis, and D. G. Luenberger, (1972), “Decomposition of Real and Reactive Power Flows: A Method Suited for On– Line Applications,” *IEEE Transactions on Power Apparatus and Systems*, 91:2 (March/April 1972) 661.

35. Luenberger, David G. (1972), “The Gradient Projection Method Along Geodesics,” *Management Science*, 18:11 (July 1972) 620–631.

36. Luenberger, David G. (1973), “An Approach to Nonlinear Programming,” *Journal of Optimization Theory and Applications*, 11:3 (1973) 219–227.

37. Luenberger, David G. (1974), “A Combined Penalty Function and Gradient Projection Method for Nonlinear Programming,” *Journal of **Optimization Theory and Applications* , 14:5 (November 1974) 477–495

38. Oren, S. S. and Luenberger, David G. (1974), “Self-Scaling Variable Metric (SSVM) Algorithms, I: Criteria and Sufficient Conditions for Scaling a Class of Algorithms,” *Management Science*, 20 (1974) 845–862.

39. Ghanem, M. and D. Luenberger (1970), “The Reduced System Method for Control Problems with Kinks,” *International Journal of Control*, 19:2 (1974) 243–256.

40. Chant, V. and D. Luenberger (1974), “A Mathematical Theory of Instruction: Instructor/Learner Interaction and Instruction Pacing,” *Journal of Mathematical Psychology*, 11:2 (1974) 132–15

41. Luenberger, David G. (1975), “A Nonlinear Economic Control Problem with a Linear Feedback Solution,” *IEEE Transactions On Automatic Control*, AC–20:2 (April 1975) 184–191.

42. Luenberger, David G. (1976), “Algorithmic Analysis in Constrained Optimization,” *SIAM–AMS Proceedings*, 9 (1976) 39–51.

43. Campbell, G., D. Luenberger, E. Ducot, and A. Levis, “On An Agricultural Policy Model with Application to Grain Markets and Reserves,” invited paper presented at the 1976 IEEE Conference on Decision and Control, Clearwater, Florida, December 1976. Also in *Proceedings 1976 IEEE Decision and Control Conference* (1976) 722–727.

44. Gabay, Daniel and David Luenberger (1976), “Efficiently Converging Minimization Methods Based on the Reduced Gradient,” *SIAM** Journal on Control and Optimization*, 14:1 (January 1976) 42–61.

45. Philippi, Bruno and David Luenberger (1977), “Neighborhood Effects and Maintenance of the Urban Housing Stock,” *Journal of Mathematical Sociology* , 5 (1977) 151–172.

46. Luenberger, David and Ami Arbel (1977), “Singular Dynamic Leontief Systems” *Econometrica*, 45:4 (May 1977) 991–995.

47. Luenberger, David G. (1977), “Dynamic Equations in Descriptor Form,” *IEEE Transactions On Automatic Control*, AC–22:3 (June 1977) 312–321.

48. Luenberger, David G. (1978), “Time-Invariant Descriptor Systems,” *Automatica*, 14 (1978) 473–480. Also presented at the 1977 JACC Conference.

49. Luenberger, David G. (1978), “Aggregation and Dual Aggregation of Positive Systems,” *Proceedings of IFAC 7th Triennial World Congress* (1978).

50. Luenberger, David G. (1978), “Linear Descriptor Variable Systems,” presented at the U.S.–Italy Symposium and published in *Lecture Notes in Economics and Mathematical Systems*, No. 162 8) 189–200.

51. Luenberger, David G. (1978), “Complete Stability of Noncooperative Games,” *IEEE Transactions On Automatic Control*, 25:4 (August 1978) 485–505.

52. Luenberger, David G. (1979), “Non–Linear Descriptor Systems,” *Journal of Economic Dynamics and Control*, 1 (1979) 219–242.

53. Luenberger, David G. (1981), “An Efficient Grading System,” Systems Economic Report #8–81, Department of Engineering–Economic Systems, Stanford University, Stanford, California, 1981.

54. Feinstein, C. and D. Luenberger (1981), “Analysis of the Asymptotic Behavior of Optimal Control Trajectories: The Implicit Programming Problem,” *SIAM** Journal on Control and Optimization*, 19:5 (September 1981) 561–585.

55. Luenberger, David G. (1982), Book Review: *Optimal Control Theory—Applications to Management Science*, Suresh Seti and Gerald Thompson, eds. in *Interfaces: A TIMS–ORSA Journal*, 12:3 (June 1982).

56. Burg, J., D. Luenberger, and D. Wenger (1982), “Estimation of Structured Covariance Matrices,” *Proceedings of the IEEE*, 70:2 (September 1982) 963– 974.

57. Yamada, T. and D. Luenberger (1985), “Generic Properties of Column-Structured Matrices,” *Linear Algebra and Its Applications*, 65 (1985) 189–206.

58. Yamada, T. and D. Luenberger (1985), “Generic Controllability Theorems for Descriptor Systems,” *IEEE Transactions on Automatic Control*, AC–30:2 (1985) 144–152.

59. Yamada, T. and D. Luenberger (1985), “Algorithms to Verify Generic Causality and Controllability of Descriptor Systems,” *IEEE Transactions On Automatic Control*, AC–30:9 (1985) 874–880.

60. Luenberger, David G. (1985), “Engineering–Economic Systems: A Problem- Solving Discipline,” *Proceedings of IFAC /IFORS Conference on Control Science and Technology for Development,* I, August 20–22, 1985, Beijing, Chinese Association of Automation for IFAC, Yang Jiachi, editor.

61. Luenberger, David G. (1985), “A Model for Science and Public Policy Programs,” in *Linking Science and Public Policy*, Proceedings of a Symposium sponsored by the University of Georgia, December 3–4, 1985, pp. 111-115. Center for Science and Public Policy, Institute of Natural Resources, University of Georgia.

62. Luenberger, David G. (1986), “Control of Linear Dynamic Market Systems,” *Journal of Economic Dynamics and Control*, 10:3 (September 1986) 339–351. (This article was presented at the XI International Symposium on Mathematical Programming, Bonn, West Germany, August 1982.)

63. Luenberger, David G. (1987), “Dynamic Equilibria for Linear Systems and Quadratic Costs,” *Automatica*, 23:1 (1987) 117–121.

64. Luenberger, David G. (1986), Citation Classic: “Observers for Multivariable Systems,” in *Contemporary Classics in Engineering and Applied Science*, compiled by Arnold Thackery, Chapter 6, p. 141, Philadelphia: ISI Press, 1986.

65. Luenberger, David G. (1988), contributor to: *Systems Control Encyclopedia: Theory, Technology, Applications*, Madan G. Singh, ed., Pergamon Press, Oxford, 1988: “Decomposition Methods” pp. 955–959; “Linear Programming: An Introduction” pp. 2835–2836; “Linear Programming: Duality” pp. 2835– 2836; “Simplex Method” pp. 4296–4299.

66. Luenberger, David G. (1989), “Boundary Recursion for Descriptor Variable Systems,” *IEEE Transactions On Automatic Control*, AC–34:3 (March 1989), 287–292.

67. Luenberger, David G. (1992), “A Double Look at Duality,” *IEEE Transactions on Automatic Control*, AC–37:10 (Oct. 1992), 1474–1482.

68. Luenberger, David G. (1992), “New Optimality Principles for Economic Efficiency and Equilibrium,” *Journal of Optimization Theory and Applications*, vol. 75, no. 2, Nov. 1992, 221–264.

69. Luenberger, David G. (1992), “Benefit Functions and Duality,” *Journal of Mathematical Economics*, 21 (1992), 461–481.

70. Luenberger, David G. (1993), “A Preference Foundation for Log Mean–Variance Criteria in Portfolio Choice Problems,” *Journal of Economic Dynamics and Control*, vol. 17, no. 5/6 (Sept./Nov. 1993), 887–906.

71. Konno, H., D. G. Luenberger and J. M. Mulvey, (eds), *Financial Engineering*, *Annals of Operations Research*, v. 45, Basel, Switzerland: J. C. Baltzer AG, (1993).

72. Cronshaw, Mark B. and David G. Luenberger (1994), “Subgame Perfect Equilibria in Infinitely Repeated Games with Perfect Monitoring and Discounting,” *Games and Economic Behavior*, 6, (1994), 220–237.

73. Luenberger, David G. (1994), “Dual Pareto Efficiency,” *Journal of Economic Theory*, vol. 62, no. 1(Feb. 1994), 70-85.

74. Luenberger, David G. (1994), “Optimality and the Theory of Value,” *Journal of Economic Theory*, 63, no. 2 (August 1994), 147-169.

75. Luenberger, David G. (1994), “Externalities and Benefits,” *Journal of Mathematical Economics*, 24, no. 2 (Feb. 1995), 159-177.

76. Luenberger, David G. and Robert R. Maxfield (1995), “Computing Economic Equilibria using Benefit and Surplus Functions,” *Computational Economics*, 8, 47-64.

77. Luenberger, David G. (1996), “Welfare from a Benefit Viewpoint,” *Economic Theory*, 7, 445-462.

78. Yates, Andrew J. and David G. Luenberger (1997), “An Efficiency Hierarchy for Constrained Economies,” *Public Finance/Finance Publiques*, vol 52, no. 2, (1997, pub. 1999), 270-288.

79. Luenberger, David G. (1997), “Products of Random Mappings,” *Journal of Ergodic Theory and Dynamic Systems*, 20, (2000), 517-529.

80. Luenberger, David G. (1998), “Products of Trees for Investment Analysis,” *Journal of Economic Dynamics and Control*, 22, (1998), 1403-1417.

81. Luenberger, David G. (1999), “Projection Pricing,” *Journal of Optimization Theory and Applications, *vol. 109, no. 1, April 2001, 1-25.

82. Luenberger, David G. (2000), “A Correlation Pricing Formula,” *Journal of Economic Dynamics and Control, *26, (2002), 1113-1126.

83. Luenberger, David G. (2001), “Arbitrage and Universal Pricing,” *Journal of Economic Dynamics and Control, *26, (2002), 1613-1628.

84. Luenberger, David G. (2003), “Pricing a Nontradeable Asset and Its Derivatives,” *Journal of Optimization Theory and Applications*, Vol. 121, No. 3, June 2004, 465-487.

85. Kuhn, Daniel and David G. Luenberger (2006), “ Analysis of the Rebalancing Frequency in Log-Optimal Portfolio Selection,” submitted for publication.

86. Luenberger, David G. (2006), “ A Lattice Methodology for Pricing Derivatives of Nontradable Assets,” in preparation*.*