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Maximize

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Maximize[f, {x, y, ...}]
maximizes f with respect to x, y, ....
Maximize[{f, cons}, {x, y, ...}]
maximizes f subject to the constraints cons.
Maximize[{f, cons}, {x, y, ...}, dom]
maximizes with variables over the domain dom, typically Reals or Integers.
  • Maximize returns a list of the form {fmax, {x->xmax, y->ymax, ...}}.
  • cons can contain equations, inequalities or logical combinations of these.
  • If f and cons are linear or polynomial, Maximize will always find a global maximum.
  • Maximize will return exact results if given exact input.
  • If Maximize is given an expression containing approximate numbers, it automatically calls NMaximize.
  • If the maximum is achieved only infinitesimally outside the region defined by the constraints, or only asymptotically, Maximize will return the supremum 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.
Maximize a univariate function:
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Maximize a multivariate function:
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Maximize a function subject to constraints:
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A maximization problem containing parameters:
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New in 5 | Last modified in 6