A linear programming proof of the second order conditions of non-linear programming
In this note we give a new, simple proof of the standard first and second order necessary conditions, under the Mangasarian-Fromovitz constraint qualification (MFCQ), for non-linear programming problems. We work under a mild constraint qualification, which is implied by MFCQ. This makes it possible to reduce the proof to the relatively easy case of inequality constraints only under MFCQ. This reduction makes use of relaxation of inequality constraints and it makes use of a penalty function. The new proof is based on the duality theorem for linear programming; the proofs in the literature are based on results of mathematical analysis. This paper completes the work in a recent note of Birbil et al. where a linear programming proof of the first order necessary conditions has been given, using relaxation of equality constraints.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Birbil, S.I. & Frenk, J.B.G. & Still, G.J., 2007. "An elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions in nonlinear programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 479-484, July.
When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:192:y:2009:i:3:p:1001-1007. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.