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65K: Mathematical programming, optimization and variational techniques


Introduction

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.

History

Applications and related fields

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).

Subfields

Parent field: 65: Numerical analysis

Browse all (old) classifications for this area at the AMS.


Textbooks, reference works, and tutorials

Software and tables

Optimization software decision tree (GAMS).

Other web sites with this focus

Selected topics at this site


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Last modified 1999/05/12 by Dave Rusin. Mail: feedback@math-atlas.org