65K: Mathematical programming, optimization and variational techniques
Optimization theory seeks to discover the means to find points where (real-valued) functions take on maximal or minimal values. (Vector-valued functions require multi-objective programming, and are almost always reduced to real-valued functions by weighting.)
We consider both the basic theory and questions regarding the encoding of the tools developed into software.
Topics in optimization also appear in Calculus of variation (typically seeking functions, curves, or other geometric objects which are optimal in some way); global analysis; and operations research (typically seeking choices of parameters to optimize some simple multivariate function). Those areas tend to emphasize the theory and application of optimization rather than the computational issues involved.
Problems in combinatorial optimization (e.g. the Traveling Salesman Problem), in which the domain (feasible set) is discrete are treated in 05: Combinatorics (or specifically in 05C: Graph Theory).
Parent field: 65: Numerical analysis
Browse all (old) classifications for this area at the AMS.
Optimization software decision tree (GAMS).