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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:

Minimize or maximize a function:

Minimize or maximize a function of several variables:

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Constrained Optimization

Find extrema that satisfy certain criteria.

Minimize or maximize a function subject to a constraint:

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Local Extrema

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

Find local minima or maxima:

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