Skip to main content
    • Aa
    • Aa


  • Yongyang Cai (a1), Kenneth L. Judd (a2), Thomas S. Lontzek (a3), Valentina Michelangeli (a4) and Che-Lin Su (a5)...

A nonlinear programming formulation is introduced to solve infinite-horizon dynamic programming problems. This extends the linear approach to dynamic programming by using ideas from approximation theory to approximate value functions. Our numerical results show that this nonlinear programming is efficient and accurate, and avoids inefficient discretization.

Corresponding author
Address correspondence to: Yongyang Cai, Hoover Institution, Stanford, CA 94305, USA; e-mail:
Hide All
Cai, Judd, Lontzek, and Michelangeli note with great sadness the passing of Che-Lin Su this past July. We thank him for his contributions. We are grateful to the editors and anonymous reviewers for their insightful comments and suggestions. We particularly thank Philipp Renner for his many helpful comments. Cai and Judd gratefully acknowledge NSF support (SES-0951576). The views expressed herein are those of the authors and do not necessarily reflect the views of the Bank of Italy.
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

D. Blackwell (1965) Discounted dynamic programming. Annals of Mathematical Statistics 36 (1), 226235.

R. Bojanic and F. Cheng (1989) Rate of convergence of Bernstein polynomials for functions with derivatives of bounded variation. Journal of Mathematical Analysis and Applications 141, 136151.

Y. Cai and K.L. Judd (2010) Stable and efficient computational methods for dynamic programming. Journal of the European Economic Association 8 (2–3), 626634.

Y. Cai and K.L. Judd (2012) Dynamic programming with shape-preserving rational spline Hermite interpolation. Economics Letters 117 (1), 161164.

Y. Cai and K.L. Judd (2013) Shape-preserving dynamic programming. Mathematical Methods of Operations Research 77 (3), 407421.

Y. Cai and K.L. Judd (2014) Advances in numerical dynamic programming and new applications. In Karl Schmedders and Kenneth L. Judd (eds.), Handbook of Computational Economics, Vol. 3, Chap. 8. Elsevier.

Y. Cai and K.L. Judd (2015) Dynamic programming with Hermite approximation. Mathematical Methods of Operations Research 81, 245267.

J.M. Carnicer and J.M. Pena (1993) Shape preserving representations and optimality of the Bernstein basis. Advances in Computational Mathematics 1 173196.

D.P. De Farias and B. Van Roy (2003) The linear programming approach to approximate dynamic programming. Operations Research 51 (6), 850865.

W.J. Den Haan , K.L. Judd , and M. Juillard (2011) Computational suite of models with heterogeneous agents: II. Multi-country real business cycle models. Journal of Economic Dynamics and Control 35, 175177.

R.T. Farouki (2012) The Bernstein polynomial basis: A centennial retrospective. Computer Aided Geometric Design 29, 379419.

T.N.T. Goodman (1989) Shape preserving representations. In T. Lyche and L.L. Schumaker (eds.), Mathematical Methods in Computer Aided Geometric Design, pp. 333351. Boston: Academic Press.

M. Juillard and S. Villemot (2011) Multi-country real business cycle models: Accuracy tests and test bench. Journal of Economic Dynamics and Control 35, 178185.

E. Polak (1997) Optimization: Algorithms and Consistent Approximations. New York: Springer.

J. Rust (1996) Numerical dynamic programming in economics. In H. Amman , D. Kendrick , and J. Rust (eds.), Handbook of Computational Economics, Vol. 1, Chap. 14. Elsevier North Holland.

J. Rust (2008) Dynamic programming. In S.N. Durlauf and L.E. Blume (eds.), New Palgrave Dictionary of Economics, 2nd ed. Palgrave Macmillan.

M.A. Trick and S.E. Zin (1997) Spline approximations to value functions—Linear programming approach. Macroeconomic Dynamics 1, 255277.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Macroeconomic Dynamics
  • ISSN: 1365-1005
  • EISSN: 1469-8056
  • URL: /core/journals/macroeconomic-dynamics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 63 *
Loading metrics...

Abstract views

Total abstract views: 260 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd September 2017. This data will be updated every 24 hours.