NMinimize
A numeric global minimum of f over a BOUNDED interval, as {value, {x -> point}} -- dense sampling plus a golden-section refinement, not an exact answer.
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NMinimize!NMinimize({f, cons}, x)the numeric global minimum of f over the bounded interval cons implies, for any real-valued f (not just the exact core Minimize covers).Typed signatures
| Type | Package | Applies |
|---|---|---|
(tuple<expression, expression>, list<symbol> | symbol) -> expression | analytic | always |
Details
- Method: sample f at 201 points across the interval (endpoints included), then refine the best sample with a golden-section search bracketed by its two neighbours (or use it as-is when the best sample IS an endpoint, with no interior bracket to refine into). Converges to a bracket width under 1e-11 (relative to the interval).
- Always numeric -- unlike Minimize, never returns an exact closed form, and works on any real-valued f, not just a recognized shape.
- Requires an explicit BOUNDED constraint:
NMinimize(f, x)alone declines, since an unconstrained numeric search has no principled starting box to invent. A constraint with an unbounded side (x >= a with no upper bound) also declines. - Declines on more than one variable.
- A function that packs more variation into the interval than the 201-point grid resolves (many tightly-spaced local minima, or a spike narrower than the grid) can still be missed -- a real limitation of a sampling-based search, not hidden here.
Examples
About
| Examples | 2 |
|---|---|
| Checked against | Wolfram Language 2 differ |
| Crosswalk | Wolfram Language |