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ConstrainedMax

  • ConstrainedMax[ f , inequalities , x , y , ... ] finds the global maximum of f in the domain specified by the inequalities. The variables x, y, ... are all assumed to be non-negative.
  • ConstrainedMax returns a list of the form , x -> , y -> , ... , where is the maximum value of f in the specified domain, and , , ... give the point at which the maximum is attained.
  • ConstrainedMax implements linear programming. It can always get a result so long as f and the inequalities you specify depend only linearly on the variables x, y, ... . The inequalities can contain no parameters other than the explicit variables you specify. The inequalities cannot involve complex numbers.
  • ConstrainedMax returns unevaluated if the inequalities are inconsistent.
  • ConstrainedMax returns an infinite result if the value of f is unbounded in the domain specified by the inequalities.
  • ConstrainedMax yields exact rational number results if f and the inequalities are specified exactly.
  • ConstrainedMax accepts both strict inequalities of the form lhs < rhs, and non-strict ones of the form lhs <= rhs. It also accepts equalities of the form lhs == rhs.
  • When ConstrainedMax returns rational number results, it assumes that all inequalities are not strict. Thus, for example, ConstrainedMax may return x->1/2, even though strict inequalities allow only .
  • ConstrainedMax finds approximate numerical results if its input contains approximate numbers. The option Tolerance specifies the tolerance to be used for internal comparisons. The default is Tolerance->Automatic, which does exact comparisons for exact numbers, and uses tolerance for approximate numbers.
  • See the Mathematica book: Section 3.9.9.
  • See also Implementation NotesA.9.44.23MainBookLinkOldButtonDataA.9.44.23.
  • See also: LinearProgramming, FindMinimum.
  • Related package: Statistics`NonlinearFit`.

    Further Examples

    This computes the max of the function under the constraints and .

    In[1]:=

    Out[1]=