Optimization and numerical methods
Objectives
Demonstrate the existence and uniqueness of a minimizer. ; Solve an unconstrained optimization problem using first-order optimality conditions. ; Solve a constrained optimization problem using Karush-Kuhn-Tucker conditions. ; Implement heuristics to numerically solve an optimization problem.
Course outline
1. Optimization: Review of differential calculus, linear algebra, and topology. General information on optimization and examples. ; Existence of a solution to an optimization problem. ; Characterization of the solution to an optimization problem (necessary and sufficient conditions). ; Solving an optimization problem using the Lagrange multiplier method. ; 2. Numerical Methods: Gradient and projected gradient methods. ; Newton’s methods for unconstrained problems.
Prerequisites
Linear algebra: matrix calculus, spectral theory. ; Differential calculus: notion of derivative, function of several variables. ; Element of topology: continuity, compactness, concept of neighborhood, open/closed.