Quadratic Support Functions in Quadratic Bilevel Problems

Oleg Khamisov ()
Additional contact information
Oleg Khamisov: Melentiev Energy Systems Institute SB RAS

A chapter in Operations Research Proceedings 2017, 2018, pp 105-110 from Springer

Abstract: Abstract We consider bilevel problem in the following formulation. The follower problem is a convex quadratic problem which linearly depends on the leader variable. The leader problem is a quadratic problem. We are looking for an optimistic solution. Optimal value function of the follower problem is used to reformulate bilevel problem as a standard (one-level) optimization problem. By this way we obtain a nonconvex multiextremal problem with implicit nonconvex constraint generated by the optimal value function. We show how to construct an explicit piecewise quadratic function which is support to the optimal value function at a given point. Usage of the support functions allows us to approximate the implicit one-level problem by a number of explicit nonconvex quadratic problems. In our talk we describe an iterative procedure based on such approximation.

Keywords: Bilevel problem; Optimal value function; Quadratic support function; Explicit global optimization problem (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-319-89920-6_15

Ordering information: This item can be ordered from
http://www.springer.com/9783319899206

DOI: 10.1007/978-3-319-89920-6_15

Access Statistics for this chapter

More chapters in Operations Research Proceedings from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().