First order solutions in conic programming

Mirjam Dür; Bolor Jargalsaikhan; Georg J. Still

doi:10.1007/s00186-015-0513-1

First order solutions in conic programming

Mirjam Dür, Bolor Jargalsaikhan, Georg J. Still

Discrete Mathematics and Mathematical Programming

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

3 Citations (Scopus)

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Abstract

We study the order of maximizers in linear conic programming (CP) as well as stability issues related to this. We do this by taking a semi-infinite view on conic programs: a linear conic problem can be formulated as a special instance of a linear semi-infinite program (SIP), for which characterizations of the stability of first order maximizers are well-known. However, conic problems are highly special SIPs, and therefore these general SIP-results are not valid for CP. We discuss the differences between CP and general SIP concerning the structure and results for stability of first order maximizers, and we present necessary and sufficient conditions for the stability of first order maximizers in CP.

Original language	English
Pages (from-to)	123-142
Number of pages	20
Journal	Mathematical methods of operations research
Volume	82
Issue number	2
DOIs	https://doi.org/10.1007/s00186-015-0513-1
Publication status	Published - Oct 2015

Keywords

EWI-26412
IR-98155
METIS-315000
n/a OA procedure

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AU - Jargalsaikhan, Bolor

AU - Still, Georg J.

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N2 - We study the order of maximizers in linear conic programming (CP) as well as stability issues related to this. We do this by taking a semi-infinite view on conic programs: a linear conic problem can be formulated as a special instance of a linear semi-infinite program (SIP), for which characterizations of the stability of first order maximizers are well-known. However, conic problems are highly special SIPs, and therefore these general SIP-results are not valid for CP. We discuss the differences between CP and general SIP concerning the structure and results for stability of first order maximizers, and we present necessary and sufficient conditions for the stability of first order maximizers in CP.

AB - We study the order of maximizers in linear conic programming (CP) as well as stability issues related to this. We do this by taking a semi-infinite view on conic programs: a linear conic problem can be formulated as a special instance of a linear semi-infinite program (SIP), for which characterizations of the stability of first order maximizers are well-known. However, conic problems are highly special SIPs, and therefore these general SIP-results are not valid for CP. We discuss the differences between CP and general SIP concerning the structure and results for stability of first order maximizers, and we present necessary and sufficient conditions for the stability of first order maximizers in CP.

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KW - IR-98155

KW - METIS-315000

KW - n/a OA procedure

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EP - 142

JO - Mathematical methods of operations research

JF - Mathematical methods of operations research

IS - 2

ER -

First order solutions in conic programming

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