The solution of Rough Bilevel Nonlinear Programming Problem by using Trust-Region Penalty Method

Elsisy, M. A.; Abo-Elnaga, Y.; Zaky, Hany Nasry; Alsobky, Wageda I.; ELhelow, K

doi:10.1088/1742-6596/2847/1/012003

The solution of Rough Bilevel Nonlinear Programming Problem by using Trust-Region Penalty Method

Document Type : Original Article

Authors

10.1088/1742-6596/2847/1/012003

Abstract

This paper, the rough bilevel nonlinear programming problem (RBNPP) is discussed taking into consideration which level is more important than the other. BNPP is transformed into a crisp unconstrained programming problem. A trust-region method is used to ensure the global convergence of the algorithm. The mechanism of solving RBNPP is presented. There are many situations of roughness in these problems are discussed. The solution procedures for solving all roughness situations are introduced based on the new proposed methodology. The de􀏐initions of solutions are de􀏐ined in all different situations. Also, we show the de􀏐inition of the fully optimal solution of the BNPPs. Finally, numerical examples are