A stability theorem in nonlinear bilevel programming.
In this short paper, we are concerned with the stability of nonlinear bilevel programs. A stability problem is proven and an example is given to illustrate this theorem.
A symmetry problem in the calculus of variations
We consider the integral functional , , where , , is a nonempty bounded connected open subset of with smooth boundary, and is a convex, differentiable function. We prove that if admits a minimizer in depending only on the distance from the boundary of , then must be a ball.
A synthesis of time-optimal controls in the presence of saturated singular arcs.
A theorem of the alternative and a two-function minimax theorem.
A topological asymptotic analysis for the regularized grey-level image classification problem
The aim of this article is to propose a new method for the grey-level image classification problem. We first present the classical variational approach without and with a regularization term in order to smooth the contours of the classified image. Then we present the general topological asymptotic analysis, and we finally introduce its application to the grey-level image classification problem.
A unified optimality condition for eigenvalue problems
A variational convergence that yields chattering systems
A variational model for urban planning with traffic congestion
We propose a variational model to describe the optimal distributions of residents and services in an urban area. The functional to be minimized involves an overall transportation cost taking into account congestion effects and two aditional terms which penalize concentration of residents and dispersion of services. We study regularity properties of the minimizers and treat in details some examples.
A variational model for urban planning with traffic congestion
We propose a variational model to describe the optimal distributions of residents and services in an urban area. The functional to be minimized involves an overall transportation cost taking into account congestion effects and two aditional terms which penalize concentration of residents and dispersion of services. We study regularity properties of the minimizers and treat in details some examples.
A Variational Proof of the Gauss-Bonnet Formula.
A variational solution of the A. D. Aleksandrov problem of existence of a convex polytope with prescribed Gauss curvature
In his book on convex polytopes [2] A. D. Aleksandrov raised a general question of finding variational formulations and solutions to geometric problems of existence of convex polytopes in , n ≥ 2, with prescribed geometric data. Examples of such problems for closed convex polytopes for which variational solutions are known are the celebrated Minkowski problem [2] and the Gauss curvature problem [20]. In this paper we give a simple variational proof of existence for the A. D. Aleksandrov problem...
A version of Zhong's coercivity result for a general class of nonsmooth functionals.
Ableitung hinreichender Bedingungen des Maximums oder Minimums einfacher Integrale ans der Theorie der zweiten Variation
Ableitung hinreichender Bedingungen des Maximums oder Minimums einfacher Integrale ans der Theorie der zweiten Variation
About stability of equilibrium shapes
We discuss the stability of "critical" or "equilibrium" shapes of a shape-dependent energy functional. We analyze a problem arising when looking at the positivity of the second derivative in order to prove that a critical shape is an optimal shape. Indeed, often when positivity -or coercivity- holds, it does for a weaker norm than the norm for which the functional is twice differentiable and local optimality cannot be a priori deduced. We solve this problem for a particular but significant example....
Adaptive control of system entropy
Adaptive tracking via pinning in networks of nonidentical nodes
We investigate the control of dynamical networks for the case of nodes, that although different, can be make passive by feedback. The so-called V-stability characterization allows for a simple set of stabilization conditions even in the case of nonidentical nodes. This is due to the fact that under V-stability characterization the dynamical difference between node of a network reduces to their different passivity degrees, that is, a measure of the required feedback gain necessary to make the node...
Additional signals in linear discrete-time control systems. III. Additional disturbance feedforward
Adherence of minimizers for dual convergences
Adjoint differential inclusions in necessary conditions for the minimal trajectories of differential inclusions