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

• Published in: Computational & applied mathematics Vol. 37; no. 1; pp. 1 - 26
• Main Authors: Tawhid, Mohamed A., Gu, Wei-Zhe, Tran, Benjamin
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2018; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Applied physics; Computational mathematics; Computational Mathematics and Numerical Analysis; Descent; Economic models; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Generalized FB function; GCP function; 90C33; Unconstrained minimization; Merit function; 90C56; Regularity conditions; Generalized complementarity problem; Descent algorithm
• ISSN: 0101-8205; 2238-3603; 1807-0302
• DOI: 10.1007/s40314-016-0328-6

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 C 1 . 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.