Abstract
Given a feasible point for a nonlinear programming problem, we investigate the structure of the feasible set near that point. Under the constraint qualification called regularity, we show how to compute the tangent cone to the feasible set, and to produce feasible arcs with prescribed first and second derivatives. In order to carry out these constructions, we show that a particular way of representing the feasible set (as a system of equations with constrained variables) is particularly useful. We also give fairly short proofs of the first-order and second-order necessary optimality conditions in very general forms, using the arc constructions mentioned above.
Keywords
- Nonlinear Programming
- Regular Point
- Tangent Cone
- Constraint Qualification
- Nonlinear Programming Problem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
O. L. Mangasarian and S. Fromovitz, The Fritz John necessary optimality conditions in the presence of equality and inequality constraints. J. Math. Anal. Appl. 17 (1967), pp. 37–47.
J.-P. Penot, On regularity conditions in mathematical programming. Math. Programming Studies 19 (1982), pp. 167–199.
S. M. Robinson, Stability theory for systems of inequalities, Part II: Differentiable nonlinear systems. SIAM J. Numer. Anal. 13 (1976), pp. 497–513.
R. T. Rockafellar, Convex Analysis. Princeton University Press, Princeton, NJ, 1970.
H. F. Weinberger, Conditions for a local Pareto optimum. Typescript, ca. 1974.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Robinson, S.M. (1983). Local structure of feasible sets in nonlinear programming, part I: Regularity. In: Numerical Methods. Lecture Notes in Mathematics, vol 1005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0112538
Download citation
DOI: https://doi.org/10.1007/BFb0112538
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12334-7
Online ISBN: 978-3-540-40967-0
eBook Packages: Springer Book Archive
