VariationalCalculus[Convex] - determine whether an integrand is convex
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Calling Sequence
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Convex(f, t, x(t))
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Parameters
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f
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expression in t, x(t), and x'(t)
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t
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independent variable
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x(t)
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unknown function (or list of functions)
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Description
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The Convex(f, t, x(t)) command determines if the integrand is convex.
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If the integrand is convex, the functional is globally minimized by extremals (solutions of the Euler-Lagrange equations).
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For a convex integrand, the output is an expression sequence containing two items:
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Hessian matrix
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Logical expression that is true iff the Hessian is positive semidefinite, which proves that J is a minimum
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If the integrand is not convex, Maple returns false.
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If LinearAlgebra[IsDefinite] cannot determine the convexity, the output is an expression sequence containing two items:
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Hessian matrix
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unevaluated call to IsDefinite
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If an error occurs in the execution of LinearAlgebra[IsDefinite], only the Hessian matrix is returned.
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The arithmetic negation makes the Hessian negative semidefinite.
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Examples
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>
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