Introductory description

To introduce general algorithms for convex and non-convex optimization problems arising in various application areas such as financial portfolio optimization, energy system planning, and engineering design optimization, and their computational aspects using a numerical software tool such as Matlab.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Module introduction with examples of several optimization problems in various application areas such as financial portfolio optimization, energy system planning, and engineering design optimization, and review of mathematical background materials (linear algebra, calculus-derivatives, etc.).
Introduction to a software for modelling and solving optimization problems.
Optimality conditions.
Unconstrained optimization.
Quadratic programming.
Constrained optimization.
Discrete optimization and exact methods.
Heuristics.
Global optimization.
Multi-objective optimization.

We plan to cover various applications such as financial portfolio optimization, energy system planning, and engineering design optimization, and several solution algorithms.

Learning outcomes

By the end of the module, students should be able to:

• Derive general optimality conditions for convex optimization problems.
• Apply numerical algorithms for unconstrained and constrained convex optimization problems.
• Apply exact methods for discrete optimization problems with general non-linear convex objective as well heuristics methods.
• Understand global optimization methods.

Indicative reading list

• G. Calafiore and L. El Ghaoui, Optimization Models, Cambridge Publications, 2014
• P. Venkataraman, Applied Optimization with Matlab Programming, Wiley, 2nd Edition, 2009
• J. Nocendal and S. Wright, Numerical Optimization, Springer, 2nd Edition, 2000
• C. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Dover Publications, 1998
• A. E. Eiben and J. E. Smith, Introduction to Evolutionary Computing, Springer 2015

Subject specific skills

Use Matlab or similar numerical software to solve optimization problems using numerical algorithms and builtin/add-on optimization solver.

Transferable skills

Distinguish between convex and non-convex optimization problems and different solution techniques.