Advances and Applications in Discrete Mathematics

The Advances and Applications in Discrete Mathematics is a prestigious peer-reviewed journal indexed in the Emerging Sources Citation Index (ESCI). It is dedicated to publishing original research articles in the field of discrete mathematics and combinatorics, including topics such as graphs, coding theory, and block design. The journal emphasizes efficient and powerful tools for real-world applications and welcomes expository articles that highlight current developments in the field.

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DP-GP OPTIMIZATION: A GEOMETRIC PROGRAMMING APPROXIMATION TECHNIQUEFOR CURSE OF DIMENSIONALITY IN DYNAMIC PROGRAMMING AND ITS REAL-LIFE APPLICATION

Authors

  • Harrison O. Amuji
  • Geoffrey U. Ugwuanyim
  • Christy C. Nwachi
  • Obioma G. Onukwube
  • Edward E. Eke
  • Iheanyi C. Obinwanne
  • Louisa N. Amaechi
  • Uzoamaka G. Chris-Ejiogu

Keywords:

dynamic programming, curse of dimensionality, geometric programming, optimal cost for decision making, optimal allocation policy

DOI:

https://doi.org/10.17654/0974165825037

Abstract

In this paper, we develop an optimization method for solving the problem of the curse of dimensionality in dynamic programming. The method has the advantage of providing a cost for decision-making and eliminates the curse of dimensionality, which restricts the application of dynamic programming to only small classes of problems and, therefore, restricts the real-life application of dynamic programming. We established some relationships between geometric programming and dynamic programming parameters. We applied the method to a problem on course allocation and obtained the cost for course allocation and the optimal decision policy to be (0.1, 0.2, 1, 3).

Received: October 24, 2024
Accepted: March 7, 2025

References

[1] A. O. Esogbuo and B. R. Marks, Non-serial dynamic programming - a survey, Operational Research Quarterly 25 (1974), 253-265.

[2] D. P. De Farias and B. Van-Roy, The linear programming approach to approximate dynamic programming, Oper. Res. 51 (2003), 850-865.

[3] U. Doraszelski and K. L. Judd, Avoiding the curse of dimensionality in dynamic stochastic games, The Economic Society 3 (2012), 53-93.

[4] J. Fernandez-Villaverde, G. Nuno, G. Sorg-Langhans and M. Vogler, Solving high-dimensional dynamic programming problems using deep learning, Economic and Computer Science (2020), 1-48.

[5] M. Avriel and A. C. Williams, Complimentary geometric programming, SIAM J. Appl. Math. 19 (1970), 125-141.

[6] S. Boyd, S. J. Kim, L. Vandenberghe and A. Hassibi, A tutorial on geometric programming, Optimization in Engineering 8 (2007), 67-127.

[7] R. J. Duffin, E. L. Peterson and C. Zener, Geometric programming - theory and application, SIAM Rev. 10 (1968), 235-236.

[8] H. O. Amuji, F. I. Ugwuowo, W. I. E. Chukwu and P. I. Uche, A modified generalized inverse method for solving geometric programming problems with extended degrees of difficulties, Int. J. Oper. Res. 38 (2020), 19-30.

[9] H. O. Amuji, G. U. Ugwuanyim and C. O. Nwosu, A solution to geometric programming problems with negative degrees of difficulty, Advances and Applications in Discrete Mathematics 26(2) (2021), 221-230.

[10] H. O. Amuji, G. U. Ugwuanyim, C. J. Ogbonna, H. C. Iwu and B. N. Okechukwu, The usefulness of dynamic programming in course allocation in the Nigerian Universities, Open Journal of Optimization 6 (2017), 176-186.

[11] H. O. Amuji, F. I. Ugwuowo, C. C. Nwachi, B. N. Okechukwu and I. O. Okeoma, On exact optimal solution to geometric programming problems, Advances and Applications in Discrete Mathematics 41(5) (2024), 429-439.

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Published

2025-08-06

Issue

Vol. 42 No. 6 (2025)

Section

Articles

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How to Cite

DP-GP OPTIMIZATION: A GEOMETRIC PROGRAMMING APPROXIMATION TECHNIQUEFOR CURSE OF DIMENSIONALITY IN DYNAMIC PROGRAMMING AND ITS REAL-LIFE APPLICATION. (2025). Advances and Applications in Discrete Mathematics, 42(6), 583-596. https://doi.org/10.17654/0974165825037

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