Descent methods for a class of generalized variational inequalities

作者：Panicucci Barbara; Pappalardo Massimo^*; Passacantando Mauro

来源：Computational Optimization and Applications, 2010, 45(2): 415-425.

DOI：10.1007/s10589-008-9230-5

• Generalized variational inequality
• Set-valued map
• Gap function
• Descent method

In this paper we propose a class of differentiable gap functions in order to formulate a generalized variational inequality (GVI) problem, involving a set-valued map with closed and convex graph, as an optimization problem. We also show that under appropriate assumptions on the set-valued map, any stationary point of the equivalent optimization problem is a global optimal solution and solves the GVI. Finally, we describe descent methods for solving the optimization problem equivalent to the GVI and we prove its global convergence.

• 出版日期2010-3