The branch of mathematical programming concerned with the theory and methods for solving problems of optimization of non-linear functions on sets given by non-linear constraints (equalities and inequalities).
The principal difficulty in solving problems in non-linear programming is their multi-extremal nature, while the known numerical methods for solving them in the general case guarantee convergence of minimizing sequences to local extremum points only.
The best studied branch of non-linear programming is convex programming, the problems in which are characterized by the fact that every local minimum point is a global minimum.
|||W.I. Zangwill, "Nonlinear programming: a unified approach" , Prentice-Hall (1969)|
|||V.G. Karmanov, "Mathematical programming" , Moscow (1975) (In Russian)|
|||E. Polak, "Computational methods in optimization: a unified approach" , Acad. Press (1971)|
|[a1]||M. Minoux, "Mathematical programming: theory and algorithms" , Wiley (1986)|
Non-linear programming. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Non-linear_programming&oldid=38638