Finite element estimates for a class of nonlinear variational inequalities.
Finite Element Methods for Nonlinear Shell Analysis.
Finite Element Solution of Nonlinear Elliptic Problems.
Finite energy maps from Riemannian polyhedra to metric spaces.
Finite-difference approximation of energies in fracture mechanics
Finite-differences discretizations of the Mumford-Shah functional
Finite-differences discretizations of the mumford-shah functional
About two years ago, Gobbino [21] gave a proof of a De Giorgi's conjecture on the approximation of the Mumford-Shah energy by means of finite-differences based non-local functionals. In this work, we introduce a discretized version of De Giorgi's approximation, that may be seen as a generalization of Blake and Zisserman's “weak membrane” energy (first introduced in the image segmentation framework). A simple adaptation of Gobbino's results allows us to compute the Γ-limit of this discrete functional...
Finite-dimensionality of information states in optimal control of stochastic systems: a Lie algebraic approach
In this paper we introduce the sufficient statistic algebra which is responsible for propagating the sufficient statistic, or information state, in the optimal control of stochastic systems. Certain Lie algebraic methods widely used in nonlinear control theory, are then employed to derive finite- dimensional controllers. The sufficient statistic algebra enables us to determine a priori whether there exist finite-dimensional controllers; it also enables us to classify all finite-dimensional controllers....
Finiteness of the number of ends of minimal submanifolds in euclidean space.
Finite-step relaxed hybrid steepest-descent methods for variational inequalities.
Finite-tight sets
We introduce two notions of tightness for a set of measurable functions - the finite-tightness and the Jordan finite-tightness with the aim to extend certain compactness results (as biting lemma or Saadoune-Valadier’s theorem of stable compactness) to the unbounded case. These compactness conditions highlight their utility when we look for some alternatives to Rellich-Kondrachov theorem or relaxed lower semicontinuity of multiple integrals. Finite-tightness locates the great growths of a set of...
First and Second Order Necessary Optimality Conditions for Discrete Optimal Control Problems
First integrals for problems of calculus of variations on locally convex spaces.
First Integrals in the Discrete Variational Calculus
First Order Characterizations of Pseudoconvex Functions
First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the generalized directional derivative.
First variation of the general curvature-dependent surface energy
We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the mean curvature of the surface. Energies of this form have applications in many areas, such as materials science, biology and image processing. Often one is interested in finding a surface that minimizes such an energy, which entails finding its first variation with respect to perturbations of the surface. We present a concise derivation...
First variation of the general curvature-dependent surface energy
We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the mean curvature of the surface. Energies of this form have applications in many areas, such as materials science, biology and image processing. Often one is interested in finding a surface that minimizes such an energy, which entails finding its first variation with respect to perturbations of the surface. We present a concise derivation...
First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints
2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.The constrained optimization problem min f(x), gj(x) ≤ 0 (j = 1,…p) is considered, where f : X → R and gj : X → R are nonsmooth functions with domain X ⊂ Rn. First-order necessary and first-order sufficient optimality conditions are obtained when gj are quasiconvex functions. Two are the main features of the paper: to treat nonsmooth problems it makes use of Dini derivatives; to obtain more sensitive conditions, it admits directionally...
Fixed point theorems and variational inequalities with non-compact sets.
Fixed points and minimax inequalities.