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	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 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

• 65K05: Mathematical programming, See also 90Cxx
• 65K10: Optimization and variational techniques, See also 49Mxx, 93B40
• 65K99: None of the above but in this section

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

• Pointer to global optimization code
• Pointer to codes for optimization and linear programming.
• Pointer, citations for global optimization
• Pointer to list of recommended optimization software
• Pointer to optimization server (NEOS).
• Various methods of nonlinear optimization: pointer to software, citation.
• Limitations of optimization methods; software
• Code: sample Genetic Algorithm for optimization
• Levenberg-Marquardt non-linear optimization.
• Pointer to pointer(!) on simulated annealing (references, code) See also http://www.cs.cmu.edu/afs/cs/project/ai-repository/ai/areas/anneal/0.html
• What is simulated annealing? (for optimization). Includes pointers to software.
• Pros and cons of variant conjugate gradient methods
• Conjugate gradient methods of optimization.
• Pointer to exposition of conjugate-gradient method of optimization.
• Citation for conjugate-gradient method of optimization.
• Pointers to original work and tutorials on the conjugate-gradient method.
• Summary of the Uzawa method for optimization of convex functions.
• Announcement of TOMLAB, a Matlab-based optimization environment.
• Invisible hand algorithms for optimization
• Making initial guesses for local optimization procedures