Special issue on applications of variational inequality problems

Abstract

I am very pleased to see the completion of this special issue of Optimization and Engineering: Applications of Variational Inequality Problems. Over the past several decades, variational inequalities have attracted a great deal of attention from both researchers and practitioners. It is well known that variational inequalities cover diverse disciplines in partial differential equations, optimal control, optimization, mathematical programming, mechanics, finance, operations research, engineering (dynamic rigidbody model, nonlinear obstacle problems), economics equilibrium models, and science. This special issue focus on applications of variational inequality problems. It includes 10 papers selected after a peer revision. The summaries of the 10 papers in this issue are listed below: The first paper, by Laura Scrimali, discusses time-dependent spatial price equilibrium problem. The author presents two different perspectives. First a useroptimization time-dependent model is studied. In particular, the equilibrium conditions are stated and the equivalence between the problem under consideration and an evolutionary variational inequality is proved. Afterwards, introducing control policies, the problem becomes a time-dependent spatial price equilibrium control problem from the policy-maker’s point of view and it is formulated as an evolutionary