Editing Mathematical optimization (section)

=== Necessary conditions for optimality ===
[[Fermat's theorem (stationary points)|One of Fermat's theorems]] states that optima of unconstrained problems are found at [[stationary point]]s, where the first derivative or the gradient of the objective function is zero (see [[first derivative test]]). More generally, they may be found at [[Critical point (mathematics)|critical points]], where the first derivative or gradient of the objective function is zero or is undefined, or on the boundary of the choice set. An equation (or set of equations) stating that the first derivative(s) equal(s) zero at an interior optimum is called a 'first-order condition' or a set of first-order conditions.

Optima of equality-constrained problems can be found by the [[Lagrange multiplier]] method. The optima of problems with equality and/or inequality constraints can be found using the '[[Karush–Kuhn–Tucker conditions]]'.