Nonlinear programming

Nonlinear programming optimizes an objective function subject to constraints when the objective or at least one constraint is nonlinear. Its solutions may be local or global optima.

Karush–Kuhn–Tucker conditions: Necessary conditions for constrained optimization that relate gradients, active constraints, and Lagrange multipliers. They characterize candidate optima when differentiable constraints satisfy suitable regularity conditions.
Feasible region: The set of points satisfying all constraints in an optimization problem. Nonlinear constraints can make this set curved, disconnected, or empty.
Optimal power flow: An optimization problem that determines economical and feasible operation of an electrical power network. AC power-flow equations make this a prominent nonlinear, often nonconvex, application.
Linear programming: Optimization of a linear objective subject to linear constraints. Its polyhedral geometry and mature algorithms differ sharply from general nonlinear models.
Nonconvex optimization: Optimization in which the objective or feasible region is nonconvex. It explains why nonlinear programs can have many local optima and difficult global guarantees.
Lagrange multipliers: Scalars used to combine constraints with an objective when deriving conditions for constrained extrema. They turn active constraints into terms in nonlinear programming's first-order conditions.
Local optimum: A point whose objective value is no worse than nearby feasible points. Nonlinear problems can have local optima that are not globally best.
Portfolio optimization: The selection of asset weights to balance investment goals and constraints. Risk measures and practical constraints can produce nonlinear portfolio models.
Quadratic programming: Optimization of a quadratic objective subject to linear constraints. It is a structured special case with methods that exploit quadratic objectives.
Numerical conditioning: The sensitivity of a computational problem's solution to small changes in its input. Poor conditioning can destabilize nonlinear optimization steps and make results unreliable.

Linked from 6 pages