Optimization

Probably all of us, in private and work situations, try to find the best possible solution to problems. I could for example be searching for the best wines for a gourmet dinner, looking for the quickest way home, finding the least costly stock investment, or even trying to find the best design for an airplane wing. In Latin, optimum is a conjugation of optimus, which in turn is a superlative for bonus, which means good. Optimization is about finding the best solution, given certain prerequisites or constraints.

In statistics, chemistry, biology, finance, geometry, operations research, and many other areas  we come across problems classified as optimization problems. Often, optimization is the better half of simulation. Even though optimization problems differ; they all share the objective of either minimizing or maximizing a function under given constraints. Dependent on the specific objective function being optimized and the given constraints, you have different problem types that differ both in hardness and when it comes to suitable solution methods.

The Third Norwegian Winter School on eScience will provide an introduction to a variety of subfields of optimization. We will focus on the computational aspects and also discuss examples of applications taken from the eVITA target areas. The goal is to provide the participants with basic knowledge of optimization and a familiarity with problem classes and solution methods.

The main themes are:

1. Introduction to optimization – an overview of important optimization problem types along with a brief introduction to convexity theory.
2. Algorithms for non-linear optimization – an introduction to solution methods for continuous problems with a non-linear objective function. A particular example is “PDE-constrained optimization”, where both the objective and the constraints are dependent on a state expressed through partial differential equations.
3. Convex optimization – is an important special case of non-linear optimization where the objective is convex and constraints give a convex feasible region. Many problems within data analysis, statistics, and finance can be formulated as convex optimization problems. The last 15 years have seen a thriving development in this field. Convex optimization problems can now be solved numerically in an efficient way.
4. Global optimization – a challenge with general non-linear optimization problems are a number of local optima where local optimization algorithms can get stuck. In global optimization, methods are designed and applied to avoid or escape local optima.
5. Discrete optimization – in many applications, some of the variables are constrained to have integer values that correspond to discrete choices. Examples are found in planning and scheduling problems. Although discrete optimization problems are often hard to solve, there is a large number of solution methods that can handle large such problems efficiently.
6. Handling uncertainty – some optimization problems are dependent on uncertain information. This if often the case in financial problems where future prices and demands are uncertain; also planning problems often involve uncertainty.

All lectures will be given in English. 

List of lecturers:

• Professor Geir Dahl, CMA, University of Oslo
• Professor Anders Forsgren, KTH
• Professor François Glineur, Université catholique de Louvain
• Chief Scientist Geir Hasle, SINTEF ICT
• Research Scientist Tomas Nordlander, SINTEF ICT
• Professor Janos Pinter, Bilkent University and PCS Inc.
• Professor Mikael Rönnquist, NHH
• Professor Alexander Shapiro, Georgia Tech.

The program is found here.

Lecture slides

• Geir Dahl: Introduction to optimization
• Geir Dahl: Convexity - an introduction
• Anders Forsgren: Nonlinear optimization
• François Glineur: Convex optimization - short
• François Glineur: Convex optimization - long
• Janos Pinter: Global optimization
• Mikael Rönnquist: Discrete optimization - exact methods
• Geir Hasle: Discrete optimization - heuristic methods
• Tomas  Nordlander: Constraint programming (slides)
• Tomas Nordlander: Constraint programming (phd)
• Alexander Shapiro: Stochastic programming

Registration

The deadline was December 7, 2008.
Online registration!

The participants are expected to stay at Dr. Holms Hotel, where we have reserved a limited number of rooms. Please register early. NB!  The registration is binding after the deadline.