A descent algorithm for generalized complementarity problems based on generalized Fischer-Burmeister functions

作者：Tawhid, Mohamed A.^*; Gu, Wei-Zhe; Tran, Benjamin

来源：COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37(1): 1-26.

DOI：10.1007/s40314-016-0328-6

• Generalized complementarity problem
• GCP function
• Generalized FB function
• Unconstrained minimization
• Regularity conditions
• Merit function
• Descent algorithm

We study an unconstrained minimization approach to the generalized complementarity problem GCP(f, g) based on the generalized Fischer-Burmeister function and its generalizations when the underlying functions are . Also, we show how, under appropriate regularity conditions, minimizing the merit function corresponding to f and g leads to a solution of the generalized complementarity problem. Moreover, we propose a descent algorithm for GCP(f, g) and show a result on the global convergence of a descent algorithm for solving generalized complementarity problem. Finally, we present some preliminary numerical results. Our results further give a unified/generalization treatment of such results for the nonlinear complementarity problem based on generalized Fischer-Burmeister function and its generalizations.

• 出版日期2018-3
• 单位天津大学