Nonlinear Programming is a graduate-level course that introduces the theory, algorithms, and applications of nonlinear optimization. The course covers the mathematical foundations of nonlinear programming, including convex sets, convex functions, generalized convexity, optimality conditions, constraint qualifications, and Lagrange duality. Students investigate analytical and computational methods for solving unconstrained and constrained optimization problems, emphasizing the Karush–Kuhn–Tucker conditions, duality theory, convergence analysis, line search techniques, and feasible direction methods.
The course integrates mathematical modeling, computational optimization, and current research to develop students' ability to formulate, analyze, and solve complex real-world decision-making problems using modern optimization techniques and appropriate computational tools. Through problem-solving activities, computational projects, and scholarly discussions, students strengthen their analytical reasoning, independent research skills, and professional communication, preparing them for advanced study and research in applied mathematics, engineering, operations research, data science, and related disciplines.
This course presents numerical methods for solving mathematical problems. It deals with the theory and application of numerical approximation techniques as well as their computer implementation using Python programming language. It covers linear systems, nonlinear equations, interpolation and numerical differentiation, numerical integration, spline functions, and symmetric matrix eigenvalue problems.
This course introduces computer programming using the Python programming language. Emphasis is placed on common algorithms and programming principles utilizing the standard library distributed with Python. Topics covered are: introduction to Python programming; variables and basic data structures; functions; branching statements; iteration; object-oriented programming; reading and writing data; visualization and plotting; and simulation in Python.