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ConstrainedMinLinearProgramming

ConstrainedMax

FilledSmallSquareConstrainedMax[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.

FilledSmallSquareConstrainedMax 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.

FilledSmallSquareConstrainedMax 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.

FilledSmallSquareConstrainedMax returns unevaluated if the inequalities are inconsistent.

FilledSmallSquareConstrainedMax returns an infinite result if the value of f is unbounded in the domain specified by the inequalities.

FilledSmallSquareConstrainedMax yields exact rational number results if f and the inequalities are specified exactly.

FilledSmallSquareConstrainedMax 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.

FilledSmallSquare 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 .

FilledSmallSquareConstrainedMax 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.

FilledSmallSquare See The Mathematica Book: Section 3.9.9.

FilledSmallSquare Implementation Notes: see section A.9.4.

FilledSmallSquare See also: LinearProgramming, FindMinimum.

FilledSmallSquare Related package: Statistics`NonlinearFit`.

Further Examples

ConstrainedMinLinearProgramming