Research Article
Breaking the Curse of Dimensionality Using a Recursive Dynamic Programming Framework
Issue:
Volume 11, Issue 3, September 2026
Pages:
112-119
Received:
9 August 2026
Accepted:
17 August 2026
Published:
27 August 2026
DOI:
10.11648/j.ajmcm.20261103.11
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Abstract: The resolution of optimal control problems (OCPs) in real-world applications is frequently beset by the curse of dimensionality and the inherent nonlinearity of system dynamics. This paper presents a literature framework that combines recursive relationship formulations with the principles of dynamic programming (DP) to address these challenges. The research stresses on a perspective that geared towards bridging the gap between the theoretical approach of DP and the numerical computation that demands practical applications. Dynamic programming is a method that finds solutions to larger sub-problems after the problem has been reduced to smaller ones. The main idea is to embed recursive relationships directly within the DP framework. The hypothesis is that for a significant class of OCPs, particularly those characterized by certain structural properties or separable cost functions, the optimal decision at a given state can be expressed recursively as a function of decisions made in states or stages. The Recursive Dynamic Programming (RDP), embeds a state-dependent recursive structure directly within the DP iteration, enabling a more efficient traversal of the state space and the generation of near-optimal control policies. We demonstrate the efficacy of this approach and its application to the resource-constrained problem. The approach follows derivation of an analytical and a semi-analytical recursive expression for major decision variables or for the gradient function value, which are then applied iteratively within the DP. The RDP framework is shown to significantly reduce computational overhead compared to classical DP while maintaining a high degree of solution accuracy, offering a pragmatic and scalable pathway for tackling complex OCPs prevalent in engineering and economic systems.
Abstract: The resolution of optimal control problems (OCPs) in real-world applications is frequently beset by the curse of dimensionality and the inherent nonlinearity of system dynamics. This paper presents a literature framework that combines recursive relationship formulations with the principles of dynamic programming (DP) to address these challenges. Th...
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Research Article
Trimmed Linear Moments Approach to Estimation of Type II Extreme Value Distribution
Issue:
Volume 11, Issue 3, September 2026
Pages:
120-127
Received:
2 August 2026
Accepted:
4 September 2026
Published:
20 October 2026
DOI:
10.11648/j.ajmcm.20261103.12
Downloads:
Views:
Abstract: The Type II Extreme Value distribution is widely applied in modelling extreme events in engineering, hydrology, and environmental studies. Accurate parameter estimation of this distribution remains essential, particularly under conditions of skewed data and the presence of outliers. Traditional estimation techniques such as the Method of Moments, Maximum Likelihood Estimation, and L-moments have been extensively used; however, they often exhibit limitations in efficiency, robustness, or computational stability. To address these challenges, this study examined the performance of Trimmed Linear Moments (1,1) as an alternative to conventional Linear moments for estimating the scale (σ) and shape (α) parameters of the Type II Extreme Value distribution. Monte Carlo simulation experiments were conducted for sample sizes and , and for fixed shape parameter values α = 2, 3 and 4, with scale parameters ranging from 0.3 to 1.5. the simulation was replicated 1000 times, and estimator performance was evaluated using mean squared error (MSE). The results consistently showed that both LM and TLM (1,1) estimators improved in accuracy as sample size increased, indicating asymptotic consistency. However, the TLM (1,1) method consistently produced smaller mean squared error MSE values than the conventional L-moments across all parameter settings and sample sizes. The study therefore recommends TLM (1,1) as a preferred estimation approach for modelling extreme value data.
Abstract: The Type II Extreme Value distribution is widely applied in modelling extreme events in engineering, hydrology, and environmental studies. Accurate parameter estimation of this distribution remains essential, particularly under conditions of skewed data and the presence of outliers. Traditional estimation techniques such as the Method of Moments, M...
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Alabi Taiye John
