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" Solving Variational Inequalities (VI) Problems Using the Barrier Method with a Parking Equilibrium Example " The variational inequality VI problem, is to find an x* belonging to a feasible region F, a subset of R^n, which satisfies the inequality f(x*)(x-x*)>=0 for all x in F, where f is a vector valued function from R^n into R^n. Many applied equilibrium problems can be formulated in this manner including ones that arise in transportation. A general formulation will be presented as well as a method to find these equilibriums numerically. The method will use barrier functions. A parking model will be used for illustration. |