Research Article
A Method for Problem Solving Dynamic Programming Using Quadratic Inequalities and Convex Monotonicity Theory
Kim Kwon Jun,
So Ung Bom,
Kim Hyon Chol*
Issue:
Volume 14, Issue 1, February 2026
Pages:
1-5
Received:
16 October 2025
Accepted:
31 October 2025
Published:
7 January 2026
DOI:
10.11648/j.sjams.20261401.11
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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.
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 ...
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Research Article
Unveiling the Impact of Nonlinear Modeling in Housing Price Prediction: An Empirical Comparative Study
Jie Wang,
Qiutong Yu,
Xintong Liu,
Hongli Zhu,
Qiuyu Ming,
Jiatong Dai,
Guanyu Sha,
Hanyu Xu,
Yan Zhong,
Shancheng Yu*
Issue:
Volume 14, Issue 1, February 2026
Pages:
6-15
Received:
15 November 2025
Accepted:
29 December 2025
Published:
9 January 2026
DOI:
10.11648/j.sjams.20261401.12
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Abstract: Regression analysis is a core analytical tool widely employed across diverse domains for predicting continuous outcomes, serving as a cornerstone of statistical inference and machine learning applications ranging from economic trend forecasting to healthcare risk assessment and real estate valuation. Choosing an effective regression technique is critical for accurate predictions, yet a daunting challenge for non-experts due to the wide variety of methods, each with distinct assumptions, tuning requirements and applicability boundaries. To address this dilemma, this study conducts a rigorous empirical comparison of five popular regression techniques—Ordinary Least Squares (OLS), Ridge regression, Lasso regression, Elastic Net, and Polynomial regression—applied to house price prediction using two benchmark datasets: the classic Boston Housing dataset and the comprehensive California Housing dataset. A multi-dimensional evaluation framework was adopted, including quantitative metrics (Mean Squared Error (MSE) and coefficient of determination () and qualitative diagnostics (residual analysis and Quantile-Quantile (QQ) plots) to assess prediction accuracy and error distribution. Results indicate that Polynomial regression consistently achieves superior performance across both datasets, highlighting its effectiveness in capturing the complex nonlinear relationships inherent in housing data. Ridge, Lasso, and Elastic Net provide comparable but lower performance, with strengths in mitigating multicollinearity rather than enhancing nonlinear fitting. OLS yields acceptable baseline results but less robust performance when confronted with real-world nonlinearities. These findings offer clear practical guidance for non-experts seeking reliable “out-of-the-box” regression techniques, and contribute valuable insights to assist practitioners in model selection for real-world predictive tasks without extensive tuning.
Abstract: Regression analysis is a core analytical tool widely employed across diverse domains for predicting continuous outcomes, serving as a cornerstone of statistical inference and machine learning applications ranging from economic trend forecasting to healthcare risk assessment and real estate valuation. Choosing an effective regression technique is cr...
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