The syllabus for the course can be found HERE.

The TimeEdit schedule can be found HERE.

Other important information about the course can be found on the Canvas home page and under the page Program and detailed information.

Course PM

Purpose

The purpose of this basic course in optimization is to provide

• knowledge of some important classes of optimization problems and of application areas of optimization modelling and methods;
• practice in describing relevant parts of a real-world problem in a mathematical optimization model;
• an understanding of necessary and sufficient optimality criteria, of their consequences, and of the basic mathematical theory upon which they are built;
• examples of optimization algorithms that are naturally developed from this theory, their convergence analysis, and their application to practical optimization problems.

Content

The main focus of the course is on optimization problems in continuous variables; it builds a foundation for the analysis of an optimization problem. We can roughly separate the material into the following areas:

• Convex analysis: convex set, polytope, polyhedron, cone, representation theorem, extreme point, Farkas Lemma, convex function
• Optimality conditions and duality: global/local optimum, existence and uniqueness of optimal solutions, variational inequality, Karush-Kuhn-Tucker (KKT) conditions, complementarity conditions, Lagrange multiplier, Lagrangian dual problem, global optimality conditions, weak/strong duality
• Linear programming (LP): LP models, LP algebra and geometry, basic feasible solution (BFS), the Simplex method, termination, LP duality, optimality conditions, strong duality, complementarity, interior point methods, sensitivity analysis
• Nonlinear optimization methods: direction of descent, line search, (quasi-)Newton method, Frank--Wolfe method, gradient projection, exterior and interior penalty, sequential quadratic programming

We also touch upon other important problem areas within optimization, such as integer programming and network optimization.

Prerequisites

Passed courses on analysis (in one and several variables) and linear algebra; familiarity with matrix/vector notation and calculus, differential calculus.

Reading Chapter 2 in the course book (see syllabus or home page) provides a partial background, especially to the mathematical notation used and most of the important basic mathematical terminology.

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