Название: Advances on Mathematical Modeling and Optimization with Its Applications
Автор: Gunjan Mukherjee, Biswadip Basu Mallik, Rahul Kar
Издательство: CRC Press
Серия: Emerging Technologies
Год: 2024
Страниц: 279
Язык: английский
Формат: pdf (true)
Размер: 22.2 MB

Advances on Mathematical Modeling and Optimization with Its Applications discusses optimization, equality, and inequality constraints and their application in the versatile optimizing domain. It further covers non-linear optimization methods such as global optimization, and gradient-based non-linear optimization, and their applications.

Modern technology is entirely dependent on the data‑driven approach, which needs mathematical aid, especially in the fields of symbolic computation dealing with the real world issues. With the passing days and gradual escalation of research and its outcomes, Artificial Intelligence and Machine learning have gained much momentum in the research fields. Such improvement of technological fields could not be possible without the mathematical concept. The wide scope of application has the wide scope of application in various areas of development and can be implemented in its own area of interest. The core of AI and Machine Learning has become immensely dependent on the statistics and application of statistical models. Significant light has been shed on the solution and interpretation of fundamental relationships between the models and their behavior thanks to the complex mathematical foundation and its built‑in equation base. the statistical procedures, such as data variable correlations. Samples, populations, and hypotheses are all used in statistical modeling.

Math has become a part of our everyday life. From the minute we wake up to the moment we go to bed, we use mathematics in every aspect of our lives. The exhaustive contribution of mathematical aspects and applicative knowledge has become research worthy due to the invention and discoveries of many advanced sorts of theorems, Whether a person is Data Scientist, Data Analyst, or Machine Learning Engineer, “Mathematics” should be a key focus of the studies. Whatever the fields of research in science and technology are, it is inevitable to think about various streams with the application of mathematics. Mathematics has become the bedrock of many new kinds of inventions in the aforementioned fields. All real world business and data‑driven applications require mathematics as a fundamental building block. From analyzing corporate transactions to figuring out how to expand in the day‑to‑day market, from calculating future stock estimates to estimating future sales, math is used in almost every facet of business. In a range of industries, such as retail, manufacturing, and information technology, math applications are used to offer a solid perspective in terms of sales, production, product intake, compensation paid, and market predictions, among other things. Therefore, mathematics has a real grasp on all sorts of technological fields to set up a relational bridge with the allied attributes of such technological overgrowths.

Artificial Intelligence (AI) and Machine Learning (ML) are hot topics in the computer world, and for good reason. They help companies streamline operations and unearth data so that they can make better business decisions. The business growth is directly or indirectly managed by the proper trend analysis and the predictive approach of growth to the ultimate level of development. They’re boosting almost every industry by allowing employees to work more effectively, and they’re fast becoming a critical piece of technology for businesses to remain competitive with others. Python is the most popular computer program for applying mathematical and statistical methods to AI development and applications. Therefore, we have demonstrated the applications of Python in different applications of mathematics in AI in this book.

• Discusses important topics including multi-component differential equations, geometric partial differential equations, and computational neural systems.
• Covers linear integer programming and network design problems, along with an application of the mixed integer problems.
• Discusses constrained and unconstrained optimization, equality, and inequality constraints, and their application in the versatile optimizing domain.
• Elucidates the application of statistical models, probability models, and transfer learning concepts.
• Showcases the importance of multi-attribute decision modeling in the domain of image processing and soft computing.

The text is primarily for senior undergraduate and graduate students, and academic researchers in the fields of mathematics, statistics, and Computer Science.