Nonlinear programming

From DDWiki

(Redirected from NLP)
Jump to: navigation, search

Nonlinear programming refers to optimization problems of the form:

minimize f(\mathbf{x})
with respect to \mathbf{x}
subject to \mathbf{g(x) \leq 0}
\mathbf{h(x)=0}
\mathbf{x}\in\Re^n

where n is a positive integer. If f(\mathbf{x}) and \mathbf{g(x)} are convex functions of the vector \mathbf{x} and \mathbf{h(x)} is an affine function of the vector \mathbf{x}, then the problem is a convex NLP (an important subclass of NLPs).

Contents

Theory


Methods

Because nonconvex NLPs may in general have multiple local minima, methods that ensure global solutions employ branch and bound methods that rely on convex underestimation of the objective and constraint functions. Global optima can generally only be found when valid convex underestimators can be generated automatically, such as for factorable functions.

Generally, local minima to NLPs can be found using modified versions of methods for solving convex NLPs.

Software


References

References

  • Bazaraa, Mokhtar S. and Shetty, C. M. (1993) Nonlinear programming. Theory and algorithms. John Wiley & Sons.
  • Bertsekas, D.P., 1995, Nonlinear programming, Athena Scientific, Belmont, MA.
  • Papalambros, P.Y. and D.J. Wilde, 2000, Principles of optimal design: modeling and computation, Cambridge University Press, New York.
Retrieved from "http://ddl.me.cmu.edu/ddwiki/index.php/Nonlinear_programming"
Personal tools