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...

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Veröffentlicht in:AIMS mathematics Jg. 7; H. 4; S. 5534 - 5562
Hauptverfasser: El-Sobky, B., Ashry, G.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: AIMS Press 2022
Schlagworte:
das scaling matrix
global convergence
newton's method
nonlinear bilevel programming problem
trust-region technique
ISSN:2473-6988, 2473-6988
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Zusammenfassung: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