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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.
  • Minimize returns a list of the form {fmin, {x->xmin, y->ymin, ...}}.
  • 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.
  • xElementIntegers can be used to specify that a particular variable can take on only integer values.
  • Even if the same minimum is achieved at several points, only one is returned.
EXAMPLESCLOSE ALL
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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