Global and Local Maxima

A local maximum is the best option in your immediate neighborhood but not the best option overall (the global maximum). Hill-climbing optimization—always moving upward from where you are—can trap you at a local peak when a much higher peak exists elsewhere. Reaching the global maximum often requires going downhill first (accepting short-term losses) to escape the local trap and find the higher peak.

When to use it

When incremental improvements are yielding diminishing returns. When considering a major strategic pivot. When someone says 'we're already the best' but the market is shifting. When feeling trapped by current success.

How it can help

Explains why incremental improvement sometimes leads to mediocrity and why disruption requires accepting temporary decline. Helps leaders distinguish between optimization (climbing the current hill) and innovation (finding a higher hill). Essential for career decisions, business pivots, and strategy shifts.