Optimization Condition

First Order Necessary Condition(FONC)

Geometry Illustration

FONC for interior case

Example

Second order necessary condition(SONC)

SONC for interior case

The necessary conditions are not sufficient

Second-order sufficient condition (SOSC)

Example

Remarks on roles of optimality(最优性) conditions

Reference

Optimization method - Standford University

https://www.youtube.com/results?search_query=convex+function