An Active-Set Fischer–Burmeister Trust-Region Algorithm to Solve a Nonlinear Bilevel Optimization Problem
In this paper, the Fischer–Burmeister active-set trust-region (FBACTR) algorithm is introduced to solve the nonlinear bilevel programming problems. In FBACTR algorithm, a Karush–Kuhn–Tucker (KKT) condition is used with the Fischer–Burmeister function to transform a nonlinear bilevel programming (NBL...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/8/412 |
| _version_ | 1797445347025354752 |
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| author | Bothina Elsobky Gehan Ashry |
| author_facet | Bothina Elsobky Gehan Ashry |
| author_sort | Bothina Elsobky |
| collection | DOAJ |
| description | In this paper, the Fischer–Burmeister active-set trust-region (FBACTR) algorithm is introduced to solve the nonlinear bilevel programming problems. In FBACTR algorithm, a Karush–Kuhn–Tucker (KKT) condition is used with the Fischer–Burmeister function to transform a nonlinear bilevel programming (NBLP) problem into an equivalent smooth single objective nonlinear programming problem. To ensure global convergence for the FBACTR algorithm, an active-set strategy is used with a trust-region globalization strategy. The theory of global convergence for the FBACTR algorithm is presented. To clarify the effectiveness of the proposed FBACTR algorithm, applications of mathematical programs with equilibrium constraints are tested. |
| first_indexed | 2024-03-09T13:24:28Z |
| format | Article |
| id | doaj.art-8e2e81c849a04558a5cf900e180b1a33 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T13:24:28Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-8e2e81c849a04558a5cf900e180b1a332023-11-30T21:25:51ZengMDPI AGFractal and Fractional2504-31102022-07-016841210.3390/fractalfract6080412An Active-Set Fischer–Burmeister Trust-Region Algorithm to Solve a Nonlinear Bilevel Optimization ProblemBothina Elsobky0Gehan Ashry1Department of Mathematics, Faculty of Science, Alexandria University, Alexandria 5424041, EgyptDepartment of Mathematics, Faculty of Science, Alexandria University, Alexandria 5424041, EgyptIn this paper, the Fischer–Burmeister active-set trust-region (FBACTR) algorithm is introduced to solve the nonlinear bilevel programming problems. In FBACTR algorithm, a Karush–Kuhn–Tucker (KKT) condition is used with the Fischer–Burmeister function to transform a nonlinear bilevel programming (NBLP) problem into an equivalent smooth single objective nonlinear programming problem. To ensure global convergence for the FBACTR algorithm, an active-set strategy is used with a trust-region globalization strategy. The theory of global convergence for the FBACTR algorithm is presented. To clarify the effectiveness of the proposed FBACTR algorithm, applications of mathematical programs with equilibrium constraints are tested.https://www.mdpi.com/2504-3110/6/8/412a bilevel optimization problemFischer–Burmeister functiona Karush–Kuhn–Tucker conditionsactive-set strategytrust-region strategyglobal convergence |
| spellingShingle | Bothina Elsobky Gehan Ashry An Active-Set Fischer–Burmeister Trust-Region Algorithm to Solve a Nonlinear Bilevel Optimization Problem Fractal and Fractional a bilevel optimization problem Fischer–Burmeister function a Karush–Kuhn–Tucker conditions active-set strategy trust-region strategy global convergence |
| title | An Active-Set Fischer–Burmeister Trust-Region Algorithm to Solve a Nonlinear Bilevel Optimization Problem |
| title_full | An Active-Set Fischer–Burmeister Trust-Region Algorithm to Solve a Nonlinear Bilevel Optimization Problem |
| title_fullStr | An Active-Set Fischer–Burmeister Trust-Region Algorithm to Solve a Nonlinear Bilevel Optimization Problem |
| title_full_unstemmed | An Active-Set Fischer–Burmeister Trust-Region Algorithm to Solve a Nonlinear Bilevel Optimization Problem |
| title_short | An Active-Set Fischer–Burmeister Trust-Region Algorithm to Solve a Nonlinear Bilevel Optimization Problem |
| title_sort | active set fischer burmeister trust region algorithm to solve a nonlinear bilevel optimization problem |
| topic | a bilevel optimization problem Fischer–Burmeister function a Karush–Kuhn–Tucker conditions active-set strategy trust-region strategy global convergence |
| url | https://www.mdpi.com/2504-3110/6/8/412 |
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