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Sufficient optimality conditions in bilevel programming

Sufficient optimality conditions in bilevel programming
Sufficient optimality conditions in bilevel programming
This paper is concerned with the derivation of first- and second-order sufficient optimality conditions for optimistic bilevel optimization problems involving smooth functions. First-order sufficient optimality conditions are obtained by estimating the tangent cone to the feasible set of the bilevel program in terms of initial problem data. This is done by exploiting several different reformulations of the hierarchical model as a single-level problem. To obtain second-order sufficient optimality conditions, we exploit the so-called value function reformulation of the bilevel optimization problem, which is then tackled with the aid of second-order directional derivatives. The resulting conditions can be stated in terms of initial problem data in several interesting situations comprising the settings where the lower level is linear or possesses strongly stable solutions.
bilevel optimization, first-order sufficient optimality conditions, second-order directional derivatives
0364-765X
Mehlitz, Patrick
eecbbf4c-dc3f-44d5-b448-3053f23874f4
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Mehlitz, Patrick
eecbbf4c-dc3f-44d5-b448-3053f23874f4
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e

Mehlitz, Patrick and Zemkoho, Alain (2021) Sufficient optimality conditions in bilevel programming. Mathematics of Operations Research. (doi:10.1287/moor.2021.1122).

Record type: Article

Abstract

This paper is concerned with the derivation of first- and second-order sufficient optimality conditions for optimistic bilevel optimization problems involving smooth functions. First-order sufficient optimality conditions are obtained by estimating the tangent cone to the feasible set of the bilevel program in terms of initial problem data. This is done by exploiting several different reformulations of the hierarchical model as a single-level problem. To obtain second-order sufficient optimality conditions, we exploit the so-called value function reformulation of the bilevel optimization problem, which is then tackled with the aid of second-order directional derivatives. The resulting conditions can be stated in terms of initial problem data in several interesting situations comprising the settings where the lower level is linear or possesses strongly stable solutions.

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1911.01647 - Accepted Manuscript
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More information

In preparation date: 2019
Accepted/In Press date: 5 October 2020
e-pub ahead of print date: 22 March 2021
Keywords: bilevel optimization, first-order sufficient optimality conditions, second-order directional derivatives

Identifiers

Local EPrints ID: 436121
URI: http://eprints.soton.ac.uk/id/eprint/436121
ISSN: 0364-765X
PURE UUID: 935a81d1-484f-4335-86ab-395c50e0a04e
ORCID for Alain Zemkoho: ORCID iD orcid.org/0000-0003-1265-4178

Catalogue record

Date deposited: 29 Nov 2019 17:30
Last modified: 22 Nov 2021 03:07

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Contributors

Author: Patrick Mehlitz
Author: Alain Zemkoho ORCID iD

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