A log-exponential regularization  method for a mathematicalprogram with general vertical complementarity constraints

Jie Zhang; Shuang Lin; Li-Wei Zhang

doi:10.3934/jimo.2013.9.561

Article Contents

2013, Volume 9, Issue 3: 561-577. Doi: 10.3934/jimo.2013.9.561

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A log-exponential regularization method for a mathematical program with general vertical complementarity constraints

1.
School of Mathematics, Liaoning Normal University, Dalian, 116029
2.
School of information Science and Engineering, Dalian Polytechnic University, Dalian, 116029

Received: February 29, 2012

Revised: February 28, 2013

Published: June 2013

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Abstract

Based on the log-exponential function, a regularization method is proposed for solving a mathematical program with general vertical complementarity constraints (MPVCC) considered by Scheel and Scholtes (Math. Oper. Res. 25: 1-22, 2000). With some known smoothing properties of the log-exponential function, a difficult MPVCC is reformulated as a smooth nonlinear programming problem, which becomes solvable by using available nonlinear optimization software. Detailed convergence analysis of this method is investigated and the results obtained generalize conclusions in Yin and Zhang (Math. Meth. Oper. Res. 64: 255-269, 2006). An example of Stackelberg game is illustrated to show the application of this method.

Keywords:

Log-exponential regularization,
mathematical program with general vertical complementarity constraints,
Stackelberg game.

Mathematics Subject Classification: Primary: 90C30; Secondary: 90C46, 90C47.

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References

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