scholarly journals A global solution method for semivectorial bilevel programming problem

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1619-1627 ◽  
Author(s):  
Yue Zheng ◽  
Jiawei Chen ◽  
Xiaogang Cao
Keyword(s):  
Programming Problem ◽  
Global Solution ◽  
Penalty Function ◽  
Bilevel Programming ◽  
Original Problem ◽  
Solution Method ◽  
Numerical Results ◽  
Exact Penalty Function ◽  
Exact Penalty ◽  
Bilevel Programming Problem

In this paper, we consider a class of semivectorial bilevel programming problem. An exact penalty function is proposed for such a problem. Based on this penalty function, an algorithm, which can obtain a global solution of the original problem, is presented. Finally, some numerical results illustrate its feasibility.

Smoothing Approximation to the New Exact Penalty Function with Two Parameters

2021 ◽  
pp. 2140010
Author(s):  
Jing Qiu ◽  
Jiguo Yu ◽  
Shujun Lian
Keyword(s):  
Global Solution ◽  
Penalty Function ◽  
Original Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Exact Penalty ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Nonlinear Inequality ◽  
Two Parameters

In this paper, we propose a new non-smooth penalty function with two parameters for nonlinear inequality constrained optimization problems. And we propose a twice continuously differentiable function which is smoothing approximation to the non-smooth penalty function and define the corresponding smoothed penalty problem. A global solution of the smoothed penalty problem is proved to be an approximation global solution of the non-smooth penalty problem. Based on the smoothed penalty function, we develop an algorithm and prove that the sequence generated by the algorithm can converge to the optimal solution of the original problem.

A New Coordination Model for Ill-Posed Bilevel Programming Problem

2013 ◽  
Vol 411-414 ◽  
pp. 1943-1947 ◽  
Author(s):  
Shi Hui Jia ◽  
Yue Zheng
Keyword(s):  
Programming Problem ◽  
Bilevel Programming ◽  
Numerical Results ◽  
Bilevel Programming Problem ◽  
Coordination Model ◽  
Linear Bilevel Programming ◽  
Ill Posed

This paper studied the leader how to motivate the follower to maximize its interests for ill-posed linear bilevel programming problem. We first presented a coordination model and gived its corresponding penalty problem. Under some conditions, we established the result on the existence of the solution. Then, an algorithm was developed to obtain a coordination solution to the original bilevel programming problem. Finally, numerical results show that the proposed method is feasible.

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