Authors: Anirudh Kulkarni, Meera Joshi, R. Venkatesh
Abstract: Optimization and optimal control play a central role in modern science, engineering, and management decision-making. From designing efficient industrial systems to controlling complex dynamical processes, these methodologies aim to identify the best possible solution under given constraints. Optimization focuses on selecting optimal values of decision variables, while optimal control extends these ideas to systems evolving over time. This paper presents a comprehensive review of fundamental concepts, mathematical formulations, classical and modern methods, and real-world applications of optimization and optimal control. Both unconstrained and constrained optimization techniques are discussed, along with optimal control problems governed by differential equations. The paper also highlights numerical approaches, computational challenges, and recent developments in the field. Through examples, tables, and discussions, this review aims to provide a structured understanding suitable for researchers and postgraduate students.
Keywords: Optimization, Optimal Control, Mathematical Programming, Dynamic Systems, Numerical Methods
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