Examples for

Optimization

Optimization is the study of minimizing and maximizing real-valued functions. Symbolic and numerical optimization techniques are important to many fields, including machine learning and robotics. Wolfram|Alpha has the power to solve optimization problems of various kinds using state-of-the-art methods.
Global Optimization

Find global extrema or find the absolute maximum or minimum of a function.

Find global extrema:

extrema (-4 x + x^2) e^(-x^2)

Minimize or maximize a function:

minimize x^4-x
maximize x(1-x)e^x

Minimize or maximize a function of several variables:

maximize 5 + 3x - 4y - x^2 + x y - y^2
minimize (4 - x^2 - 2y^2)^2
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Constrained Optimization

Find extrema that satisfy certain criteria.

Minimize or maximize a function subject to a constraint:

minimize x^5 - 3x^4 + 5 over [0,4]
maximize e^x sin y on x^2+y^2=1
maximize xyz in x^2+2y^2+3z^2<=1
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Local Extrema

Scan for extrema that qualify as extrema only in a certain subdomain.

Find local minima or maxima:

local maxima x^5 - 10x^3 + 30x
local minima x^2/40 + cos(x) + 1
local extrema sin x^2
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