Non-linear programming

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.

References

[1]	W.I. Zangwill, "Nonlinear programming: a unified approach" , Prentice-Hall (1969)
[2]	V.G. Karmanov, "Mathematical programming" , Moscow (1975) (In Russian)
[3]	E. Polak, "Computational methods in optimization: a unified approach" , Acad. Press (1971)

References

[a1]	M. Minoux, "Mathematical programming: theory and algorithms" , Wiley (1986)