A smooth non linear optimization problem or nonlinear programming (NLP) is one in which the objective or at least one of the constraints is a smooth nonlinear function of the decision variables. An example of a smooth nonlinear function is: 2 X12 + X23 + log X3. ...where X 1, X 2 and X 3 are decision variables.

In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function.

In smooth optimization (linear programming, integer linear programming, and nonlinear programming), the objective functions are smooth and continuous, meaning you can draw them without lifting your pencil from the paper.

If the graph of the function’s derivative also contains no breaks, then the original function is called a smooth function. If it does contain breaks, then the original function is non-smooth. Every discontinuous function is also non-smooth.

Jul 1, 2015 · Both the $l_1$ and $l_{\infty}$ norms can be expressed as a 'max-function'. There is a non-smooth calculus in which the derivative is replaced by a generalized gradient (cf. subdifferential in convex analysis). Many of the familiar results have equally familiar counterparts.

The problem is called a nonlinear programming problem (NLP) if the objective function is nonlinear and/or thefeasible region is determined by nonlinear constraints.

Continuous optimization problems are typi-cally solved using algorithms that generate a se-quence of values of the variables, known as it-erates, that converge to a solution of the prob-lem.

If F,G,Hare nonlinear and smooth, we speak of a nonlinear programming problem (NLP). Only in few special cases a closed form solution exists. Use an iterative algorithm to find an approximate solution. Problem may be parametric, and some (or all) functions depend on a fixed parameter p∈Rp, e.g. model predictive control. 1.

Dec 12, 2005 · Nonlinear Programming (NLP) minimize f(x) subject to h i(x)= 0, i ∈ E, h i(x)≥ 0, i ∈ I. NLP is convex if • h i ’s in equality constraints are affine; • h i ’s in inequality constraints are concave; • f is convex; NLP is smooth if • All are twice continuously differentiable.

Nonlinear programming is a direct extension of linear programming, when we replace linear model functions by nonlinear ones. Numerical algorithms and computer programs are widely applicable and commercially available as black box software.