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## 42111 Static and Dynamic Optimization

### Danish title:

Statisk og dynamisk optimering

5

### Course type:

 Advanced course Taught under open university

E3A

### Scope and form:

Lectures and project work

13 weeks

04231.02711

### General course objectives:

To give a well-founded knowledge, both theoretically and practically, of static and dynamic optimization models for data-based decision making. The students will be able to formulate and solve operations research and technical-economic models, and to appreciate the interplay between optimization models and the real-life problems describbed by these.

### Learning objectives:

A student who has met the objectives of the course will be able to:
• Analyze a given problem in order to formulate an optimization model.
• Formulate and analyze models as these are met in static and dynamic optimization.
• Describe and explain the assumptions underlying models and computations.
• Analyze an optimization problem in order to identify an a.ppropriate solution method
• Understand and - using software - solve systems of equations for given optimization problems.
• Interpret the solutions from a given optimization model.
• Describe and explain the mathematical background for the applied solution methods.
• Perform sensitivity analysis as part of the evalutaiton of what-if scenarios in decision making.
• Make use of the possibilities for sensitivity analysis in standard optimization software.

### Content:

Static optimization: Linear programming and duality, Convexity and optimality, Karush-Kuhn-Tucker conditions, Lagrangian duality, Solution methods. Examples of economic and technical applications: production planning, portfolio planning. Dynamic optimization: Control theory, Pontriagin's maximum principle, dynamic programming, Bellman's optimality principle. Examples of economic and technical applications: pipe line problem, production planning, economic models.

### Course literature:

Course notes and slides.
Hillier & Lieberman: Intro. to OR, ch. Nonlinear Programming (in 9th and 8th Ed., ch. 12)

### Responsible:

Niels Kjølstad Poulsen, 322, 126, (+45) 4525 3356,
Mette Gamst, 426, 56, (+45) 4525 4541,
Richard Martin  Lusby, 426, 052, (+45) 4525 3084,

### Department:

42 DTU Management Engineering

### Department involved:

02 Department of Informatics and Mathematical Modeling

http://www.imm.dtu.dk/courses/02711

At CampusNet

### Keywords:

optimization, non-linear programming, optimal control
Last updated: April 23, 2012

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