Nonlinear programming (NP) involves minimizing or maximizing a nonlinear objective function subject to bound constraints, linear constraints, or nonlinear constraints, where the constraints can be inequalities or equalities. Example problems in engineering include analyzing design tradeoffs, selecting optimal designs, and computing optimal trajectories.
Unconstrained nonlinear programming is the mathematical problem of finding a vector \(x\) that is a local minimum to the nonlinear scalar function \(f(x)\). Unconstrained means that there are no restrictions placed on the range of \(x\)
The following algorithms are commonly used for unconstrained nonlinear programming:
Constrained nonlinear programming is the mathematical problem of finding a vector \(x\) that minimizes a nonlinear function \(f(x)\) subject to one or more constraints.
Algorithms for solving constrained nonlinear programming problems include:
For more information on nonlinear programming, see Optimization Toolbox™.
See also: Optimization Toolbox, Global Optimization Toolbox, linear programming, quadratic programming, integer programming, multiobjective optimization, genetic algorithm, simulated annealing, prescriptive analytics