Numerical optimization

a repository of mathematical know-how

Numerical optimization

Title: *

Area of mathematics: *

A comma-separated list of areas of mathematics to which this article applies. Use ">" to tag in a subcategory. Example: Analysis > Harmonic analysis, Combinatorics

Keywords:

A comma-separated list of keywords associated with this article. Example: free group

Used in:

A comma-separated list of examples of where this technique is used. Example: Cauchy-Schwarz inequality

Parent articles:		Order

Body:

[QUICK DESCRIPTION]
Numerical optimization is a large and important part of numerical analysis,
with a great many practical applications.

We can focus on different types of problems, particularly, unconstrained and constrained (equality and inequality constrints).
Constrained problems lead to the use of Lagrange multipliers.  
The objective function (the function to minimize or maximize) can be convex, smooth, or non-smooth (and convex or not as the case may be).

Non-convex problems are generally harder than convex ones, especially as there is often a problem of local minima (or local maxima).

[PREREQUISITES]
Multivariate calculus.

[EXAMPLE]

[GENERAL DISCUSSION]

Convex vs non-convex optimization.

Convex optimization is considered easier as finding a point satisfying $\nabla f(x) = 0$ (in the unconstrained case) or satisfying the Karush--Kuhn--Tucker conditions (in the general constrained case) is sufficient to show that the point is a global minimizer. For general non-convex optimization, this is not true.

Non-convex optimization in general requires some kind of global search; unless there is some special structure to the problem, derivative information can only determine the behaviour of a function nearby.

Algorithmic issues

Numerical optimization is about the application of computational methods, and so is inherently about (numerical) algorithms.

This is a stub

A stub is an article that is not sufficiently complete to be interesting.

Notifications

File attachments

Changes made to the attachments are not permanent until you save this post. The first "listed" file will be included in RSS feeds.

Attach new file:

Images are larger than 640x480 will be resized. The maximum upload size is 1 MB. Only files with the following extensions may be uploaded: jpg jpeg gif png svg.

Revision information

Log message:

An explanation of the additions or updates being made to help other authors understand your motivations.

Numerical optimization

Recent articles

Active forum topics

Recent comments