MinValue

The global minimum VALUE of f -- Minimize's value alone, without the witnessing point.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageMinValue✓↗

MinValue(f, x)the global minimum of f over its own natural domain.

MinValue({f, cons}, x)the global minimum of f restricted to a simple interval constraint cons.

Typed signatures

Type	Package	Applies
(expression, list<symbol> | symbol) -> expression	analytic	always

Domain: Calculus

Details

• A projection of Minimize onto just the value -- same scope, same machinery; see Minimize's details for the full account.
• The one case this covers that Minimize itself declines -- Sin/Cos of an affine argument, unconstrained -- because a value alone doesn't need a witnessing point Wolfram's own choice of (among infinitely many) isn't reproducible here. Its exact amplitude, +-1, is well defined regardless.

Examples

Basic #

A quadratic's vertex value

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In$\mathrm{MinValue}(x^2-4x+3, x)$Out$-1$

With x >= 1, the boundary value

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In$\mathrm{MinValue}(\bigl\lbrack x^2, x≥1\bigr\rbrack, x)$Out$1$

The minimum of the upward parabola is $\frac{31}{8}$

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In$\mathrm{MinValue}(2x^2-3x+5, x)$Out$\frac{31}{8}$

Scope #

Cos's exact minimum value, -1 -- Minimize itself would decline this (no reproducible point)

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In$\mathrm{MinValue}(\cos(3x-1), x)$Out$-1$

Exp's infimum, even though it is never attained

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In$\mathrm{MinValue}(e^{x}, x)$Out$0$

A constrained minimum that is too hard stays unevaluated within the time limit

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In$\mathrm{TimeConstrained}(\mathrm{MinValue}(\bigl\lbrack x^2+y^2+z^2, x^2-3xyz+9z^2+y^2=e∧xyz≤π\bigr\rbrack, \bigl\lbrack x, y, z\bigr\rbrack), 60)$Out$\mathrm{MinValue}(\bigl\lbrack x^2+y^2+z^2, x^2-3xyz+9z^2+y^2=e∧xyz≤π\bigr\rbrack, \bigl\lbrack x, y, z\bigr\rbrack)$

About

Examples	6
Checked against	Wolfram Language 6 agree
Crosswalk	Wolfram Language

See also: Minimize, MaxValue, Maximize