An interior-point trust-region algorithm to solve a nonlinear bilevel programming problem

In this paper, a nonlinear bilevel programming (NBLP) problem is transformed into an equivalent smooth single objective nonlinear programming (SONP) problem utilized slack variable with a Karush-Kuhn-Tucker (KKT) condition. To solve the equivalent smooth SONP problem effectively, an interior-point N...

Full description

Saved in:

Bibliographic Details
Published in:	AIMS mathematics Vol. 7; no. 4; pp. 5534 - 5562
Main Authors:	El-Sobky, B., Ashry, G.
Format:	Journal Article
Language:	English
Published:	AIMS Press 2022
Subjects:	das scaling matrix global convergence newton's method nonlinear bilevel programming problem trust-region technique
ISSN:	2473-6988, 2473-6988
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	In this paper, a nonlinear bilevel programming (NBLP) problem is transformed into an equivalent smooth single objective nonlinear programming (SONP) problem utilized slack variable with a Karush-Kuhn-Tucker (KKT) condition. To solve the equivalent smooth SONP problem effectively, an interior-point Newton's method with Das scaling matrix is used. This method is locally method and to guarantee convergence from any starting point, a trust-region strategy is used. The proposed algorithm is proved to be stable and capable of generating approximal optimal solution to the nonlinear bilevel programming problem. A global convergence theory of the proposed algorithm is introduced and applications to mathematical programs with equilibrium constraints are given to clarify the effectiveness of the proposed approach.
ISSN:	2473-6988 2473-6988
DOI:	10.3934/math.2022307