Editing Nonlinear programming (section)

=== Analytic methods ===
Under [[differentiability]] and [[constraint qualification]]s, the [[Karush–Kuhn–Tucker conditions|Karush–Kuhn–Tucker (KKT) conditions]] provide necessary conditions for a solution to be optimal. If some of the functions are non-differentiable, [[subderivative|subdifferential]] versions of [[Karush–Kuhn–Tucker conditions|Karush–Kuhn–Tucker (KKT) conditions]] are available.<ref>
{{cite book |last=Ruszczyński |first=Andrzej |title=Nonlinear Optimization |publisher=[[Princeton University Press]] |year=2006 |isbn=978-0691119151 |location=Princeton, NJ |pages=xii+454 |mr=2199043 |author-link=Andrzej Piotr Ruszczyński}}</ref>

Under convexity, the KKT conditions are sufficient for a [[global optimum]]. Without convexity, these conditions are sufficient only for a [[local optimum]]. In some cases, the number of local optima is small, and one can find all of them analytically and find the one for which the objective value is smallest.<ref name=":0">{{Cite web |last=Nemirovsky and Ben-Tal |date=2023 |title=Optimization III: Convex Optimization |url=http://www2.isye.gatech.edu/~nemirovs/OPTIIILN2023Spring.pdf}}</ref>