Continuous Optimization
A course on Continuous Optimization  Nick Gould, STFCRAL
Optimization deals with the problem of minimising or maximising a mathematical model of an objective function such as cost, fuel consumption etc. under a set of side constraints on the domain of definition of this function. Optimization theory is the study of the mathematical properties of optimization problems and the analysis of algorithms for their solution. The aim of this course is to provide an introduction to nonlinear continuous optimization specifically tailored to the background of mathematicsl students.
The major prerequisites for the course will be some knowledge of both linear algebra and real analysis, while an appreciation of methods for the numerical solution of linear systems of equations will be helpful.
The course consists of lectures and classes, but no practicals. Students hand in solutions to six problem sheets which will be discussed in classes during the term.
Copies of the key points for each lecture, along with notes giving details of proofs of results, will be made available in advance:
1.  A gentle introduction. [key poimts: 1, 2, 4 slides per page] 
23.  Optimality conditions and why they are important. [key poimts: 1, 2, 4 slides per page] [notes: 1, 2 sides per page] 
46.  Linesearch methods for unconstrained minimization. [key points: 1, 2, 4 slides per page] [notes: 1, 2 sides per page] 
79.  Trustregion methods for unconstrained minimization. [key points: 1, 2, 4 slides per page] [notes: 1, 2 sides per page] 
1011.  Activeset methods for linearlyconstrained minimization. [key points: 1, 2, 4 slides per page] [notes: 1, 2 sides per page] 
12.  Penalty and augmented Lagrangian methods for constrained minimization. [key points: 1, 2, 4 slides per page] [notes: 1, 2 sides per page] 
1516.  Sequential quadratic programming (SQP) methods for constrained minimization. [key points: 1, 2, 4 slides per page] [notes: 1, 2 sides per page] 
Full lecture notes are available as an accompanying booklet.
These notes form a selfcontained introduction to the subject, and constitute compulsory reading assignments. Suggestions on how to improve the lecture notes are always very welcome!
The following books contain useful background material. The first is particularly recommended:

J. Nocedal and S. Wright, Numerical Optimization, Springer Verlag 1999

J. Dennis and R. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, (republished by) SIAM (Classics in Applied Mathematics 16) 1996

P. Gill, W. Murray and M. Wright, Practical Optimization, Academic Press 1981

R. Fletcher, Practical Methods of Optimization, 2nd edition Wiley 1987, (republished in paperback 2000)

A. Conn, N. Gould and Ph. Toint, TrustRegion Methods, SIAM 2000
Optimization, at its best, is featured on the following WWW sites:
 Linear programming frequentlyasked questions
 Nonlinear programming frequentlyasked questions
 The Optimization Technology Center with its guide to optimization software
 The NetworkEnabled Optimization System(NEOS)  solve optimization problems online
 A Decision Tree for Optimization Software, and associated Benchmarks for Optimization Software
 Optimization Online
 INFORMS resouces
 Mathematical Optimization Society
 SIAM