## Course syllabus

The syllabus for the course can be found here: Chalmers and GU.

The TimeEdit schedule can be found .

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 home page) provides a partial background, especially to the mathematical notation used and most of the important basic mathematical terminology.

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