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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Vydané v:	AIMS mathematics Ročník 7; číslo 4; s. 5534 - 5562
Hlavní autori:	El-Sobky, B., Ashry, G.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	AIMS Press 2022
Predmet:	das scaling matrix global convergence newton's method nonlinear bilevel programming problem trust-region technique
ISSN:	2473-6988, 2473-6988
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Popis
Shrnutí:	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