Regularity of a kind of marginal functions in Hilbert spaces

We study well-posedness of some mathematical programming problem depending on a parameter that generalizes in a certain sense the metric projection onto a closed nonconvex set. We are interested in regularity of the set of minimizers as well as of the value function, which can be seen, on one hand, as the viscosity solution to a Hamilton-Jacobi equation, while, on the other, as the minimal time in some related optimal time control problem. The regularity includes both the Fréchet differentiability of the value function and the Hölder continuity of its (Fréchet) gradient

Iterative Schemes for Nonconvex Quasi-Variational Problems with V

In this paper, we propose an extension of quasi-equilibrium problems from the convex case to the nonconvex case and from Hilbert spaces to Banach spaces. The proposed problem is called quasi-variational problem. We study the convergence of some algorithms to solutions of the proposed nonconvex problems in Banach spaces

Iterative Schemes for Nonconvex Quasi-Variational Problems with V-Prox-Regular Data in Banach Spaces

In this paper, we propose an extension of quasi-equilibrium problems from the convex case to the nonconvex case and from Hilbert spaces to Banach spaces. The proposed problem is called quasi-variational problem. We study the convergence of some algorithms to solutions of the proposed nonconvex problems in Banach spaces

IC071.dvi

Abstract In this paper we prove the existence of solutions to the following third order differential inclusion: is an upper semi-continuous set-valued mapping with G(x, y, z) ⊂ ∂ C g(z) where g : H → R is a uniformly regular function over S and locally Lipschitz and S is a ball compact subset of a separable Hilbert space H

General Existence Results for Third-Order Nonconvex State-Dependent Sweeping Process with Unbounded Perturbations

We prove the existence of solutions for third-order nonconvex state-dependent sweeping process with unbounded perturbations of the form: -A(x(3)(t))∈N(K(t,ẋ(t));  A(ẍ(t)))+F(t,x(t),ẋ(t),ẍ(t))+G(x(t),ẋ(t),ẍ(t))      a.e.  [0,T], A(ẍ(t))∈K(t,ẋ(t)), a.e.    t∈[0,T], x(0)=x0,ẋ(0)=u0, ẍ(0)=υ0, where T>0, K is a nonconvex Lipschitz set-valued mapping, F is an unbounded scalarly upper semicontinuous convex set-valued mapping, and G is an unbounded uniformly continuous nonconvex set-valued mapping in a separable Hilbert space H

Receding horizon control of a hybrid production system with deteriorating items

In this paper, a receding horizon control strategy is applied to a dynamic hybrid production system with deteriorating items. Given the current inventory level, we determine the optimal production rates to be implemented at the beginning of each of the following periods over the control horizon. The effectiveness of this approach was in the use of future information of the inventory target level and the desired production rate, which are available. Both the continuous and periodic review policies are investigated. The performances of the proposed control algorithms are illustrated by simulation