An iterative method for nonconvex equilibrium problems.
An iterative scheme with a countable family of nonexpansive mappings for variational inequality problems in Hilbert spaces.
An L2-Error Estimate for an Approximation of the Solution of a Parabolic Variational Inequality.
An L...-Estimate for the gradient of extremals.
An observability estimate for parabolic equations from a measurable set in time and its applications
This paper presents a new observability estimate for parabolic equations in , where is a convex domain. The observation region is restricted over a product set of an open nonempty subset of and a subset of positive measure in . This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.
An optimal control approach to cancer treatment under immunological activity
Mathematical models for cancer treatment that include immunological activity are considered as an optimal control problem with an objective that is motivated by a separatrix of the uncontrolled system. For various growth models on the cancer cells the existence and optimality of singular controls is investigated. For a Gompertzian growth function a synthesis of controls that move the state into the region of attraction of a benign equilibrium point is developed.
An optimal control problem for a fourth-order variational inequality
An optimal control problem is considered where the state of the system is described by a variational inequality for the operator w → εΔ²w - φ(‖∇w‖²)Δw. A set of nonnegative functions φ is used as a control region. The problem is shown to have a solution for every fixed ε > 0. Moreover, the solvability of the limit optimal control problem corresponding to ε = 0 is proved. A compactness property of the solutions of the optimal control problems for ε > 0 and their relation with the limit problem...
An optimal control problem for a generalized Boussinesq model: The time dependent case.
An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System
An optimal control problem is studied for a predator-prey system of PDE, with a logistic growth rate of the prey and a general functional response of the predator. The control function has two components. The purpose is to maximize a mean density of the two species in their habitat. The existence of the optimal solution is analyzed and some necessary optimality conditions are established. The form of the optimal control is found in some particular...
An optimal control problem for a pseudoparabolic variational inequality
We deal with an optimal control problem governed by a pseudoparabolic variational inequality with controls in coefficients and in convex sets of admissible states. The existence theorem for an optimal control parameter will be proved. We apply the theory to the original design problem for a deffection of a viscoelastic plate with an obstacle, where the variable thickness of the plate appears as a control variable.
An optimal control problem for an elliptic variational inequality
An optimal control problem for Helmholtz equation with non-local boundary conditions and quadratic funtional
An optimal control problem in economics.
An optimal shape design problem for a hyperbolic hemivariational inequality
In this paper we consider hemivariational inequalities of hyperbolic type. The existence result for hemivariational inequality is given and the existence theorem for the optimal shape design problem is shown.
An optimum design problem in magnetostatics
In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.
An Optimum Design Problem in Magnetostatics
In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.
An oriented coincidence index for nonlinear Fredholm inclusions with nonconvex-valued perturbations.
An overview of semi-infinite programming theory and related topics through a generalization of the alternative theorems.
We propose new alternative theorems for convex infinite systems which constitute the generalization of the corresponding to Gale, Farkas, Gordan and Motzkin. By means of these powerful results we establish new approaches to the Theory of Infinite Linear Inequality Systems, Perfect Duality, Semi-infinite Games and Optimality Theory for non-differentiable convex Semi-Infinite Programming Problem.
An unconstrained optimization technique for nonsmooth nonlinear complementarity problems.
Analyse de récession et résultats de stabilité d’une convergence variationnelle, application à la théorie de la dualité en programmation mathématique
Soit un espace de Banach de dual topologique . (resp. ) désigne l’ensemble des parties non vides convexes fermées de (resp. -fermées de ) muni de la topologie de la convergence uniforme sur les bornés des fonctions distances. Cette topologie se réduit à celle de la métrique de Hausdorff sur les convexes fermés bornés [16] et admet en général une représentation en terme de cette dernière [11]. De plus, la métrique qui lui est associée s’est révélée très adéquate pour l’étude quantitative...