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. Discusses important topics including multi-component differential equations, geometric partial differential equations, and computational neural systemsCovers linear integer programming and network design problems, along with an application of the mixed integer problemsDiscusses constrained and unconstrained optimization, equality, and inequality constraints, and their application in the versatile optimizing domainElucidates the application of statistical models, probability models, and transfer learning conceptsShowcases the importance of multi-attribute decision modeling in the domain of image processing and soft computingThe text is primarily for senior undergraduate and graduate students, and academic researchers in the fields of mathematics, statistics, and computer science.