OPTIMIZATION TECHNIQUES IN DATA SCIENCE: A MATHEMATICAL PERSPECTIVE

Abstract

The core function of data science depends on optimization because it provides the base for both algorithmic speed and statistical modeling and decision processes. Research examines optimization methods from a mathematical perspective through evaluations of their theoretical foundations together with their convergence attributes and calculations requirements. The research investigates classical gradient-based approaches Gradient Descent and Newton’s Method with complete convergence analysis and establishes the role of Karush-Kuhn-Tucker (KKT) conditions and Lagrange duality for analyzing convex optimization problems. The discussion focuses on non-convex optimization challenges because traditional methods fall short for these problems yet metaheuristic approaches including Simulated Annealing, Genetic Algorithms, and Particle Swarm Optimization solve complex high-dimensional problems effectively.

The study recognizes three main mathematical optimization difficulties: solving large-dimensional optimization issues and finding efficient methods for deep learning while achieving the proper balance between exploration and exploitation. Research proposals outline a strategy to connect classical and heuristic optimization methods by integrating machine learning-based techniques that create adaptive and reliable optimization models. This study produces findings that will impact data science along with artificial intelligence as well as computational mathematics since they create a foundation for upcoming developments in optimization-driven methodologies.