Continuous optimization

As a branch of applied mathematics, optimization is now ubiquitous. It was at the end of the last world war that it became truly operational, with the appearance of linear programming to organize American convoys to Europe (the "liberty ships"). It then developed strongly from the 1960s onwards, when non-linear problems could be tackled efficiently, thanks mainly to "quasi-Newton" methods.

The problems dealt with in this article belong to the field of continuous optimization, in which the variables to be optimized can take on a whole continuum of values. This is in contrast to combinatorial problems, in which the aim is to find the best among a finite set of possibilities. This article does not deal with the latter.

Continuous optimization methods are all based on the analysis of functions of several real variables, and all involve constructing an iterative sequence of approximate solutions. It is this type of method that is the subject of this article.