Minimize

Minimize[f, x]
minimizes f with respect to x.

Minimize[f, {x, y, ...}]
minimizes f with respect to x, y, ....

Minimize[{f, cons}, {x, y, ...}]
minimizes f subject to the constraints cons.

Minimize[{f, cons}, {x, y, ...}, dom]
minimizes with variables over the domain dom, typically Reals or Integers.

Details and OptionsDetails and Options

  • Minimize returns a list of the form .
  • cons can contain equations, inequalities, or logical combinations of these.
  • If f and cons are linear or polynomial, Minimize will always find a global minimum.
  • Minimize will return exact results if given exact input.
  • If Minimize is given an expression containing approximate numbers, it automatically calls NMinimize.
  • If the minimum is achieved only infinitesimally outside the region defined by the constraints, or only asymptotically, Minimize will return the infimum and the closest specifiable point.
  • If no domain is specified, all variables are assumed to be real.
  • xIntegers can be used to specify that a particular variable can take on only integer values.
  • If the constraints cannot be satisfied, Minimize returns {+Infinity, {x->Indeterminate, ...}}.
  • Even if the same minimum is achieved at several points, only one is returned.
  • Minimize[f, x, WorkingPrecision->n] uses n digits of precision while computing a result. »

ExamplesExamplesopen allclose all

Basic Examples (4)Basic Examples (4)

Minimize a univariate function:

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Minimize a multivariate function:

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Minimize a function subject to constraints:

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A minimization problem containing parameters:

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New in 5 | Last modified in 6
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