49: Calculus of variations and optimal control; optimization
Calculus of variations and optimization seek functions or geometric objects which are optimize some objective function. Certainly this includes a discussion of techniques to find the optima, such as successive approximations or linear programming. In addition, there is quite a lot of work establishing the existence of optima and characterizing them. In many cases, optimal functions or curves can be expressed as solutions to differential equations. Common applications include seeking curves and surfaces which are minimal in some sense. However, the spaces on which the analysis are done may represent configurations of some physical system, say, so that this field also applies to optimization problems in economics or control theory for example.
See also 65K (for numerical optimization), 90C (for applications of optimization to operations research, mathematical programming, etc.), 93 (for control theory in general), and 34H05 for differential equations in control problems.
Browse all (old) classifications for this area at the AMS.
Pesch, Hans Josef: "A practical guide to the solution of real-life optimal control problems" Parametric optimization. Control Cybernet. 23 (1994), no. 1-2, 7--60. MR95b:49047
Bonnans, J. Frédéric; Shapiro, Alexander: "Optimization problems with perturbations: a guided tour", SIAM Rev. 40 (1998), no. 2, 228--264 (electronic). original article.
Fraser-Andrews, G.: "Finding candidate singular optimal controls: a state of the art survey", J. Optim. Theory Appl. 60 (1989), no. 2, 173--190. MR90b:49004
GAMS listing of Optimal control software