 |
||||||||||
| Volume 6, Number 1, January 2010, pp. 3-19 | ||||||||||
| Rhoda P. Agdeppa, Nobuo Yamashita and Masao Fukushima | ||||||||||
| Key words: | ||||||||||
| stochastic affine variational inequality problem, expected residual method, regularized gap function, D-gap function, convexity, traffic equilibrium problem | ||||||||||
| Mathematices Subject Classification: 65K10, 90C15, 90B20 | ||||||||||
|
||||||||||||||||||||||||||||||||||||||||
| Abstract: | |||
| The affine variational inequality problem (AVIP) is a wide class of problems which includes the quadratic programming problems and the linear complementarity problem. In this paper, we consider AVIP under uncertainty in order to present a more realistic view of real world problems. We call such a problem the stochastic affine variational inequality problem (SAVIP). Recently, a new approach called the expected residual (ER) method has been proposed to give a reasonable solution of SAVIP. The ER method regards a minimizer of an expected residual function for the AVIP as a solution of SAVIP. Previous studies on the ER method employed the ``min'' function or the Fischer-Burmeister (FB) function. Such functions however are nonconvex in general and hence we may not get a global solution. In this paper, we employ the regularized gap function and the D-gap function to define a residual in the ER model. We also show that our proposed ER models are convex under some conditions and hence a global solution can be obtained using existing solution methods. Finally we apply our proposed model to the traffic equilibrium problem under uncertainty using a sample network. | |||
| Convex expected residual models for stochastic affine variationalinequality problems and its application to the traffic equilibrium problem | ||