An Iterative Algorithm for the Nonlinear MC² Model with Variational Inequality Method

Abstract

The multiple criteria and multiple constraint level (MC 2 ) model is a useful tool to deal with the decision programming problems, which concern multiple decision makers and uncertain resource constraint levels. In this paper, by regarding the nonlinear MC 2 problems as a class of mixed implicit variational inequalities, we develop an iterative algorithm to solve the nonlinear MC 2 problems through the resolvent operator technique. The convergence of the generated iterative sequence is analyzed and discussed by a calculation example, and the stability of Algorithm 1 is also verified by error propagation. By comparing with two other MC 2 -algorithms, Algorithm 1 performs well in terms of number of iterations and computation complexity.

Keywords

• nonlinear MC² models
• implicit variational inequality
• resolvent operator technique
• iterative algorithm