Dynamic programming is an important discipline in the fields of applied mathematics, operations, and computer science, and standard solution methods are used in various fields of engineering, economics, commerce, management, etc. Dynamic programming is that, whatever the initial state of optimality and the initial control, a sequence of subsequent controls with respect to the resulting state must be the optimal strategy. Thus, it is an optimization method that solves problems in a time-dependent process using the principle of optimality for economic problems that cannot be solved by linear programming. The continued emergence of publications describing new settings, reformulations and general theory in the development of dynamic programming demonstrates the continuing interest in the fundamental problems of dynamic programming. In this paper, we introduce an acceleration method to improve the execution time, which is the most challenging problem in solving many real-life dynamic programming problems. And we prove that the acceleration method using decision monotonicity is effective in improving the execution time when the input data is large compared to the existing method. We also consider the execution time when the mathematical model of the plant is referred to as dynamic programming and the state transition equation satisfies convex monotonicity. We have used the quadrilateral inequality and convex monotonicity theory to solve the traditional computational complexity and time-increasing problem and find reasonable solutions quickly and accurately. In this paper, we introduce an accelerated method to improve the execution time, which is the most challenging problem in solving many real-life dynamic programming problems. We define the quadrilateral inequality and convex monotonicity theory and consider the acceleration of the dynamic programming solution of the mathematical model satisfying it.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 14, Issue 1) |
| DOI | 10.11648/j.sjams.20261401.11 |
| Page(s) | 1-5 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Dynamic Programming, Acceleration, Decision Monotonicity, Algorithm, Complexity
| [1] | Moshe Sniedovich. Dynamic Programming Foundations and Principles 2nd Edition, 2012. |
| [2] | F. Frances. Yao. Speed-Up in Dynamic Programming, 2016. |
| [3] | Warren B. Powel, Approximate Dynamic Programming, 2007. |
| [4] | Huaguang Zhang, Derong Liu, Yanhong Luo, Ding Wang, Adaptive Dynamic Programming for Control, 2012. |
| [5] | Art Lew, Holger Mauch, Dynamic Programming, 2006. |
| [6] | Samir M. Koriem, T. E. Dabbous, W. S. El-Kilani, A new Petri net modeling technique for the performance analysis of discrete event dynamic systems, 2004, The journal of systems and software 72, |
| [7] | Sokol Bush Kaliaj, A functional equation arising in dynamic programming, Springer International Publishing, 2017, |
| [8] | Hamed Khaledi, Mohammad Reisi-Nafchi, Dynamic production planning model: a dynamic programming approach, 2012, |
| [9] | Fawaz Alsolami, Talha Amin, Igor Chikalov, Mikhail Moshkov, Dynamic Programming Approach for Construction of Association Rule Systems, 2016, |
| [10] | L. P. Myshlyaev, S. N. Starovatskaya, Dynamic Programming in the Presence of Indeterminacy, 2011, |
| [11] | Jiangyan Pu, Qi Zhang, Dynamic Programming Principle and Associated Hamilton-Jacobi—Bellman Equation for Stochastic Recursive Control Problem with Non-Lipschitz Aggregator, 2018, |
| [12] | Yu. V. Bugaev, S. V. Chikunov, Generalization of the Dynamic Programming Scheme, 2007, |
| [13] | Warren B. Powell, Perspectives of approximate dynamic programming, 2012, |
| [14] | E. A. Galperin, Reflections on Optimality and Dynamic Programming, 2006, |
| [15] | S. Kindermann, A. Leitão, Regularization by dynamic programming, 2007, |
APA Style
Jun, K. K., Bom, S. U., Chol, K. H. (2026). A Method for Problem Solving Dynamic Programming Using Quadratic Inequalities and Convex Monotonicity Theory. Science Journal of Applied Mathematics and Statistics, 14(1), 1-5. https://doi.org/10.11648/j.sjams.20261401.11
ACS Style
Jun, K. K.; Bom, S. U.; Chol, K. H. A Method for Problem Solving Dynamic Programming Using Quadratic Inequalities and Convex Monotonicity Theory. Sci. J. Appl. Math. Stat. 2026, 14(1), 1-5. doi: 10.11648/j.sjams.20261401.11
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.sjams.20261401.11,
author = {Kim Kwon Jun and So Ung Bom and Kim Hyon Chol},
title = {A Method for Problem Solving Dynamic Programming Using Quadratic Inequalities and Convex Monotonicity Theory},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {14},
number = {1},
pages = {1-5},
doi = {10.11648/j.sjams.20261401.11},
url = {https://doi.org/10.11648/j.sjams.20261401.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20261401.11},
abstract = {Dynamic programming is an important discipline in the fields of applied mathematics, operations, and computer science, and standard solution methods are used in various fields of engineering, economics, commerce, management, etc. Dynamic programming is that, whatever the initial state of optimality and the initial control, a sequence of subsequent controls with respect to the resulting state must be the optimal strategy. Thus, it is an optimization method that solves problems in a time-dependent process using the principle of optimality for economic problems that cannot be solved by linear programming. The continued emergence of publications describing new settings, reformulations and general theory in the development of dynamic programming demonstrates the continuing interest in the fundamental problems of dynamic programming. In this paper, we introduce an acceleration method to improve the execution time, which is the most challenging problem in solving many real-life dynamic programming problems. And we prove that the acceleration method using decision monotonicity is effective in improving the execution time when the input data is large compared to the existing method. We also consider the execution time when the mathematical model of the plant is referred to as dynamic programming and the state transition equation satisfies convex monotonicity. We have used the quadrilateral inequality and convex monotonicity theory to solve the traditional computational complexity and time-increasing problem and find reasonable solutions quickly and accurately. In this paper, we introduce an accelerated method to improve the execution time, which is the most challenging problem in solving many real-life dynamic programming problems. We define the quadrilateral inequality and convex monotonicity theory and consider the acceleration of the dynamic programming solution of the mathematical model satisfying it.},
year = {2026}
}
TY - JOUR T1 - A Method for Problem Solving Dynamic Programming Using Quadratic Inequalities and Convex Monotonicity Theory AU - Kim Kwon Jun AU - So Ung Bom AU - Kim Hyon Chol Y1 - 2026/01/07 PY - 2026 N1 - https://doi.org/10.11648/j.sjams.20261401.11 DO - 10.11648/j.sjams.20261401.11 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 1 EP - 5 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20261401.11 AB - Dynamic programming is an important discipline in the fields of applied mathematics, operations, and computer science, and standard solution methods are used in various fields of engineering, economics, commerce, management, etc. Dynamic programming is that, whatever the initial state of optimality and the initial control, a sequence of subsequent controls with respect to the resulting state must be the optimal strategy. Thus, it is an optimization method that solves problems in a time-dependent process using the principle of optimality for economic problems that cannot be solved by linear programming. The continued emergence of publications describing new settings, reformulations and general theory in the development of dynamic programming demonstrates the continuing interest in the fundamental problems of dynamic programming. In this paper, we introduce an acceleration method to improve the execution time, which is the most challenging problem in solving many real-life dynamic programming problems. And we prove that the acceleration method using decision monotonicity is effective in improving the execution time when the input data is large compared to the existing method. We also consider the execution time when the mathematical model of the plant is referred to as dynamic programming and the state transition equation satisfies convex monotonicity. We have used the quadrilateral inequality and convex monotonicity theory to solve the traditional computational complexity and time-increasing problem and find reasonable solutions quickly and accurately. In this paper, we introduce an accelerated method to improve the execution time, which is the most challenging problem in solving many real-life dynamic programming problems. We define the quadrilateral inequality and convex monotonicity theory and consider the acceleration of the dynamic programming solution of the mathematical model satisfying it. VL - 14 IS - 1 ER -
Faculty of Information Science and Technology, Kim Chaek University of Technology, Pyongyang, DPR Korea
