Course Description
This course covers both classical and modern optimization methods with applications in engineering, business, and data science — including linear programming, nonlinear optimization, integer programming, stochastic optimization, and metaheuristics.
Topics Covered
Classical Optimization
Single-variable, multivariable unconstrained, and constrained optimization.
Linear Programming
Problem formulation, graphical method, Simplex method, duality, sensitivity analysis.
Nonlinear Optimization
Gradient descent, Newton's method, conjugate gradient, quasi-Newton methods.
Integer & Combinatorial
Integer programming, branch and bound, cutting plane methods.
Stochastic Optimization
Markov decision processes, dynamic programming, robust optimization.
Metaheuristics
Genetic algorithms, simulated annealing, tabu search, particle swarm optimization.
Recommended Textbooks
Introduction to Linear Optimization
The standard graduate-level text on linear optimization.
Core TextNumerical Optimization
Comprehensive coverage of algorithms for nonlinear optimization.
Algorithms for Optimization
Modern treatment with Julia code examples.
Prerequisites
Basic linear algebra (vectors, matrices), calculus (derivatives, gradients), and fundamental probability.