By J. Talbert, H. Heng
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4 are satisfied and conclusion does not hold. 4 are satisfied and conclusion does not hold. 7. 4 is satisfied. Moreover, since conclusion can not hold. References  H. Hermes, JP. B. Lee, L. Markus, Foundations of Optimal Control Theory, John Wiley and Sons, New York, 1967.  P. Cubiotti, Application of quasi-variational inequalities to linear control systems, J. Optim. Theory Appl. 89 (1996), 101–113.  P. Cubiotti An existence theorem for generalized quasi-variational inequalities, Set-Valued Anal.
There is a total supply in each supply market where and a total demand in each demand market where Since the markets are spatially separated, units of commodity are transportated from to If we consider the excess supply and the excess demand we must have Variational Inequalities for Static Equilibrium Market… 45 We associate with each supply market a supply price and with each demand market a demand price A fixed minimal supply price (price floor) for each supply market and a fixed maximum demand price (price ceiling) for each demand market are given.
34] D. S. Womersley, A new unconstrained differentiable merit function for box constrained variational inequality problems and a damped Gauss-newton method, SIAM J. Optim. 9 (1999), 388–413.  J. Sun, G. Zhao, Global linear and local quadratic convergence of a long-step adaptive-mode interior-point method for some monotone variational inequality problems, SIAM J. Optim. 8 (1998), 123–139.  B. T. Harker, A nonsmooth Newton method for variational inequalities, I: theory, Math. Progr. 65 (1994), 151–194.