An Active-Set Fischer-Burmeister Trust-Region Algorithm to Solve a Nonlinear Bilevel Optimization Problem

被引：2
|
作者：
Elsobky, Bothina [1 ]
Ashry, Gehan [1 ]
机构：
[1] Alexandria Univ, Dept Math, Fac Sci, Alexandria 5424041, Egypt
来源：
FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 08期
关键词：
a bilevel optimization problem; Fischer-Burmeister function; a Karush-Kuhn-Tucker conditions; active-set strategy; trust-region strategy; global convergence; INTERIOR-POINT ALGORITHM; GLOBAL OPTIMIZATION; DESCENT METHOD; NCP-FUNCTIONS;
D O I：
10.3390/fractalfract6080412
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页数：29
相关论文
共 42 条
  • [1] An active-set with barrier method and trust-region mechanism to solve a nonlinear Bilevel programming problem
    El-Sobky, B.
    Ashry, G.
    Abo-Elnaga, Y.
    [J]. AIMS MATHEMATICS, 2022, 7 (09): : 16112 - 16146
  • [2] A multiplier active-set trust-region algorithm for solving constrained optimization problem
    El-Sobky, Bothina
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (03) : 928 - 946
  • [3] An active-set algorithm and a trust-region approach in constrained minimax problem
    B. EL-Sobky
    A. W. Aboutahoun
    [J]. Computational and Applied Mathematics, 2018, 37 : 2605 - 2631
  • [4] A trust-region method by active-set strategy for general nonlinear optimization
    Ji, Ying
    Zhang, Ke-Cun
    Qu, Shao-Jian
    Zhou, Ying
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 54 (02) : 229 - 241
  • [5] An active-set trust-region algorithm for solving warehouse location problem
    Abo-Elnaga, Y.
    El-Sobky, B.
    Al-Naser, L.
    [J]. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, 2017, 11 (02): : 353 - 358
  • [6] An active-set algorithm and a trust-region approach in constrained minimax problem
    EL-Sobky, B.
    Aboutahoun, A. W.
    [J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (03): : 2605 - 2631
  • [7] An interior-point trust-region algorithm to solve a nonlinear bilevel programming problem
    El-Sobky, B.
    Ashry, G.
    [J]. AIMS MATHEMATICS, 2022, 7 (04): : 5534 - 5562
  • [8] AN ACTIVE-SET INTERIOR-POINT TRUST-REGION ALGORITHM
    El-Sobky, Bothina
    [J]. PACIFIC JOURNAL OF OPTIMIZATION, 2018, 14 (01): : 125 - 159
  • [9] A penalty method with trust-region mechanism for nonlinear bilevel optimization problem
    El-Sobky, B.
    Abo-Elnaga, Y.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 340 : 360 - 374
  • [10] An active-set trust-region method for derivative-free nonlinear bound-constrained optimization
    Gratton, Serge
    Toint, Philippe L.
    Troeltzsch, Anke
    [J]. OPTIMIZATION METHODS & SOFTWARE, 2011, 26 (4-5): : 873 - 894
12345