Survey paper: Optimality conditions in smooth nonlinear programming

G. Still; Martin Streng

doi:10.1007/BF02189792

Survey paper: Optimality conditions in smooth nonlinear programming

G. Still, Martin Streng

Research output: Contribution to journal › Article › Academic › peer-review

15 Citations (Scopus)

72 Downloads (Pure)

Abstract

This survey is concerned with necessary and sufficient optimality conditions for smooth nonlinear programming problems with inequality and equality constraints. These conditions deal with strict local minimizers of order one and two and with isolated minimizers. In most results, no constraint qualification is required. The optimality conditions are formulated in such a way that the gaps between the necessary and sufficient conditions are small and even vanish completely under mild constraint qualifications.

Original language	English
Pages (from-to)	483-516
Number of pages	34
Journal	Journal of optimization theory and applications
Volume	90
Issue number	3
DOIs	https://doi.org/10.1007/BF02189792
Publication status	Published - 1996

Keywords

Nonlinear programming
Necessary and sufficient optimality conditions
Isolated minimizers
Strong and strict local minimizers

Access to Document

10.1007/BF02189792

Still1996optimalityFinal published version, 1.11 MB

Cite this

@article{0c8975e776cb4d1a9a0cc7116bfc12b4,

title = "Survey paper: Optimality conditions in smooth nonlinear programming",

abstract = "This survey is concerned with necessary and sufficient optimality conditions for smooth nonlinear programming problems with inequality and equality constraints. These conditions deal with strict local minimizers of order one and two and with isolated minimizers. In most results, no constraint qualification is required. The optimality conditions are formulated in such a way that the gaps between the necessary and sufficient conditions are small and even vanish completely under mild constraint qualifications.",

keywords = "Nonlinear programming, Necessary and sufficient optimality conditions, Isolated minimizers, Strong and strict local minimizers",

author = "G. Still and Martin Streng",

year = "1996",

doi = "10.1007/BF02189792",

language = "English",

volume = "90",

pages = "483--516",

journal = "Journal of optimization theory and applications",

issn = "0022-3239",

publisher = "Springer",

number = "3",

}

TY - JOUR

T1 - Survey paper: Optimality conditions in smooth nonlinear programming

AU - Still, G.

AU - Streng, Martin

PY - 1996

Y1 - 1996

N2 - This survey is concerned with necessary and sufficient optimality conditions for smooth nonlinear programming problems with inequality and equality constraints. These conditions deal with strict local minimizers of order one and two and with isolated minimizers. In most results, no constraint qualification is required. The optimality conditions are formulated in such a way that the gaps between the necessary and sufficient conditions are small and even vanish completely under mild constraint qualifications.

AB - This survey is concerned with necessary and sufficient optimality conditions for smooth nonlinear programming problems with inequality and equality constraints. These conditions deal with strict local minimizers of order one and two and with isolated minimizers. In most results, no constraint qualification is required. The optimality conditions are formulated in such a way that the gaps between the necessary and sufficient conditions are small and even vanish completely under mild constraint qualifications.

KW - Nonlinear programming

KW - Necessary and sufficient optimality conditions

KW - Isolated minimizers

KW - Strong and strict local minimizers

U2 - 10.1007/BF02189792

DO - 10.1007/BF02189792

M3 - Article

VL - 90

SP - 483

EP - 516

JO - Journal of optimization theory and applications

JF - Journal of optimization theory and applications

SN - 0022-3239

IS - 3

ER -

Survey paper: Optimality conditions in smooth nonlinear programming

Abstract

Keywords

Access to Document

Fingerprint

Cite this