Nonlinear optimization

In mathematics, nonlinear programming (NLP), also known as nonlinear optimization, 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. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear. Definition and discussionLet n, m, and p be positive integers. Let X be a subset of R (usually a box-constrained one), let f, gi, and hj be real-valued functions on X for each i in {1, ..., m} and each j in {1, ..., p}, with at least one of f, gi, and hj being nonlinear. A nonlinear programming problem is an optimization problem of the form minimize f(x)subject to gi(x)≤0 for each i∈{1,…,m}hj(x)=0 for each j∈{1,…,p}x∈X.{\displaystyle {\begin{aligned}{\text{minimize }}&f(x)\\{\text{subject to }}&g_{i}(x)\leq 0{\text{ for each }}i\in \{1,\dotsc ,m\}\\&h_{j}(x)=0{\text{ for