Locally Optimal

You have found a good place to stop.

Every small move makes things worse.

That sounds convincing.

It also leaves something unanswered.

In mathematics a local minimum is a point where no sufficiently nearby alternative gives a lower value.

Another valley elsewhere may go deeper.

You can be best in the neighborhood without being best on the map.

That distinction became the starting point for Locally Optimal.

We imagined a landscape with one small region singled out for attention. Contours gather around a marked point. A frame sets the neighborhood apart.

The landscape continues beyond it.

The mathematical conditions beneath the diagram give the claim its foundation. For a smooth function a zero gradient together with positive curvature in every direction is enough to establish a strict local minimum.

A precise conclusion.

Within a limited reach.

GLOBAL CLAIMS WITHHELD.

We chose this idea because there is something quietly appealing about confidence that knows its boundaries. A result can be useful. A decision can be sound.

Neither requires pretending that every possibility has been exhausted.

The point has earned its place.

The rest of the landscape remains open.

Beauty. Discovery. Depth.

Mathematical reference: Stanford — Unconstrained Optimization