An extension of the Jacobi algorithm for multi-valued mixed complementarity problems

Abstract

We consider a generalized mixed complementarity problem (MCP) with box constraints and multi-valued cost mapping. We introduce a concept of an upper Z-mapping, which generalizes the well-known concept of the single-valued Z-mapping and involves the diagonal multi-valued mappings, and suggest an extension of the Jacobi algorithm for the above problem containing a composition of such mappings. Being based on its convergence theorem, we establish several existence and uniqueness results. Some examples of the applications are also given.

Keywords:

• Mixed complementarity problem
• Multi-valued mappings
• Upper Z-mappings
• Jacobi algorithm
• Existence of solutions

Keywords:

• Mathematics Subject Classification 2000
• 90C33
• 47H04
• 49J40
• 91A40
• 91B54