Applications of mathematical systems in solving optimization problems in engineering and finance
DOI:
https://doi.org/10.71068/w7f8s746Keywords:
optimization, mathematical models, efficiency, sustainabilityAbstract
Optimization plays a key role in engineering and finance, enabling the resolution of complex problems under specific constraints. In Latin America, its application is essential for improving resource management efficiency and decision-making in uncertain scenarios. This study aims to analyze the implementation of advanced mathematical optimization models and their impact on various sectors. The methodology is based on the development and application of optimization algorithms, algebraic models, and numerical analysis, considering case studies in power grid planning, sustainable structural design, and financial portfolio management. Methods such as linear and nonlinear optimization, dynamic programming, and advanced heuristics were employed, evaluating their effectiveness in cost reduction, increased operational efficiency, and improved project sustainability. The results show that optimization significantly contributes to technological innovation and sustainable development, although it faces challenges related to computational complexity and the need for high-quality data. It was identified that the integration of artificial intelligence and high-performance computing can enhance the applicability of these models, enabling more precise and scalable solutions. This study highlights the importance of adaptive strategies to overcome technical limitations and maximize the impact of optimization in strategic sectors, fostering its adoption in resource-limited contexts and promoting decision-making based on robust mathematical models.
References
Åström, K. J., & Murray, R. M. (2012). Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press. https://www.cds.caltech.edu/~murray/books/AM08/pdf/am08-complete_28Sep12.pdf
Bazilian, M., Nussbaumer, P., Rogner, H. H., Brew-Hammond, A., Foster, V., Pachauri, S., ... & Kammen, D. M. (2012). Energy access scenarios to 2030 for the power sector in sub-Saharan Africa. Utilities Policy, 20, 1-16. https://pure.iiasa.ac.at/10020
Bazilian, M., Roques, F., Toman. Analytical Methods for Energy Diversity and Security. Elsevier. https://shop.elsevier.com/books/analytical-methods-for-energy-diversity-and-security/bazilian/978-0-08-056887-4
Bertsimas, D., & Tsitsiklis, J. N. (2014). Introduction to Linear Optimization. Athena Scientific. https://www.researchgate.net/publication/235558951_Introduction_to_Linear_Optimization#full-text
Boell, S. K., & Cecez-Kecmanovic, D. (2015). On being ‘systematic’ in literature reviews in IS. Journal of Information Technology, 30(2), 161-173. https://doi.org/10.1057/jit.2014.2
Boyd, S., & Vandenberghe, L. (2014). Convex Optimization. Cambridge University Press. https://web.stanford.edu/~boyd/cvxbook/
Bryman, A. (2016). Social Research Methods. Oxford University Press. https://global.oup.com/academic/product/social-research-methods-9780199689453
Cooper, H., Hedges, L. V., & Valentine, J. C. (2019). The Handbook of Research Synthesis and Meta-Analysis. Russell Sage Foundation. https://www.russellsage.org/publications/handbook-research-synthesis-and-meta-analysis-third-edition
Crainic, T. G., & Laporte, G. (2016). Transportation and Logistics: A Spatial Perspective. Edward Elgar Publishing. https://www.e-elgar.com/shop/gbp/transportation-and-logistics-9781785364519.html
Fabozzi, F. J., Focardi, S. M., & Kolm, P. N. (2014). Robust Portfolio Optimization and Management. Wiley. https://www.wiley.com/en-us/Robust+Portfolio+Optimization+and+Management-p-9781118001144
Fabozzi, F. J., Gupta, F., & Markowitz, H. M. (2014). The Theory and Practice of Investment Management. Wiley. https://www.wiley.com/en-us/The+Theory+and+Practice+of+Investment+Management%3A+Asset+Allocation%2C+Valuation%2C+Portfolio+Construction%2C+and+Strategies%2C+2nd+Edition-p-9781118370523
Falagas, M. E., Pitsouni, E. I., Malietzis, G. A., & Pappas, G. (2008). Comparison of PubMed, Scopus, Web of Science, and Google Scholar: strengths and weaknesses. The FASEB Journal, 22(2), 338-342. https://doi.org/10.1096/fj.07-9492LSF
Geidl, M., & Andersson, G. (2010). Optimal power flow of multiple energy carriers. IEEE Transactions on Power Systems, 25(1), 28-37. https://doi.org/10.1109/TPWRS.2006.888988
Geidl, M., & Andersson, G. (2010). Optimal power flow with renewable energy resources. IEEE Transactions on Power Systems. https://doi.org/10.1007/s00202-016-0402-5
Glover, F., & Laguna, M. (2013). Tabu Search. Springer Science & Business Media. https://doi.org/10.1007/978-1-4615-6089-0
Gough, D., Oliver, S., & Thomas, J. (2017). An Introduction to Systematic Reviews. Sage. https://uk.sagepub.com/en-gb/eur/an-introduction-to-systematic-reviews/book245742
Hastie, T., Tibshirani, R., & Friedman, J. (2017). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer. https://doi.org/10.1007/978-0-387-84858-7
Higgins, J. P., Thomas, J., Chandler, J., Cumpston, M., Li, T., Page, M. J., & Welch, V. A. (2019). Cochrane Handbook for Systematic Reviews of Interventions. John Wiley & Sons. https://training.cochrane.org/handbook
Kitchenham, B., & Charters, S. (2007). Guidelines for Performing Systematic Literature Reviews in Software Engineering. EBSE Technical Report. https://www.durham.ac.uk/media/durham-university/departments-/computer-science/research/technical-reports/2007/EBSE-2007-01.pdf
Markowitz, H., Todd, G., Sharpe, W. F., & Miller, M. H. (2016). Portfolio Selection: Efficient Diversification of Investments. Yale University Press. https://www.patrimoniohistorico.prefeitura.sp.gov.br/fill-and-sign-pdf-form/Resources/_pdfs/portfolio_selection_efficient_diversification_of_investments.pdf
Martins, J. R. R. A., & Lambe, A. B. (2013). Multidisciplinary design optimization: A survey of architectures. AIAA Journal, 51(9), 2049-2075. https://doi.org/10.2514/1.J051895
Petticrew, M., & Roberts, H. (2006). Systematic Reviews in the Social Sciences: A Practical Guide. John Wiley & Sons. https://doi.org/10.1002/9780470754887
Raiffa, H., & Schlaifer, R. (2012). Applied Statistical Decision Theory. Wiley. https://doi.org/978-0-471-38349-9
Russell, S., & Norvig, P. (2021). Artificial Intelligence: A Modern Approach. Pearson. https://www.pearson.com/en-us/subject-catalog/p/artificial-intelligence-a-modern-approach/P200000003500/9780137505135
Sterman, J. D. (2000). Business Dynamics: Systems Thinking and Modeling for a Complex World. McGraw-Hill. https://www.researchgate.net/publication/44827001_Business_Dynamics_System_Thinking_and_Modeling_for_a_Complex_World
Martinelli, L. A., & Filoso, S. (2008). Expansion of sugarcane ethanol production in Brazil: environmental and social challenges. Ecological Applications, 18(4), 885–898. https://doi.org/10.1890/07-1813.1
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