A construction of quasiconvex functions with linear growth at infinity
A contribution to methods of Exterior Penalty Functions for Nonlinear Programming
A convergence analysis of Newton's method under the gamma-condition in Banach spaces
We provide a local as well as a semilocal convergence analysis for Newton's method to approximate a locally unique solution of an equation in a Banach space setting. Using a combination of center-gamma with a gamma-condition, we obtain an upper bound on the inverses of the operators involved which can be more precise than those given in the elegant works by Smale, Wang, and Zhao and Wang. This observation leads (under the same or less computational cost) to a convergence analysis with the following...
A convergence result and numerical study for a nonlinear piezoelectric material in a frictional contact process with a conductive foundation
We consider two static problems which describe the contact between a piezoelectric body and an obstacle, the so-called foundation. The constitutive relation of the material is assumed to be electro-elastic and involves the nonlinear elastic constitutive Hencky's law. In the first problem, the contact is assumed to be frictionless, and the foundation is nonconductive, while in the second it is supposed to be frictional, and the foundation is electrically conductive. The contact is modeled with the...
A convergence result for evolutionary variational inequalities and applications to antiplane frictional contact problems
We consider a class of evolutionary variational inequalities depending on a parameter, the so-called viscosity. We recall existence and uniqueness results, both in the viscous and inviscid case. Then we prove that the solution of the inequality involving viscosity converges to the solution of the corresponding inviscid problem as the viscosity converges to zero. Finally, we apply these abstract results in the study of two antiplane quasistatic frictional contact problems with viscoelastic and elastic...
A convergence result for the Gradient Flow of ∫ |A| 2 in Riemannian Manifolds
We study the gradient flow of the L2−norm of the second fundamental form for smooth immersions of two-dimensional surfaces into compact Riemannian manifolds. By analogy with the results obtained in [10] and [11] for the Willmore flow, we prove lifespan estimates in terms of the L2−concentration of the second fundamental form of the initial data and we show the existence of blowup limits. Under special condition both on the initial data and on the target manifold, we prove a long time existence result...
A convergent algorithm for solving linear programs with an additional reverse convex constraint
A Counterexample for Some Lower Semicontinuity Results.
A counter-example to some recent existence results on implicit variational inequalities
In this note we prove that some recent results on an implicit variational inequality problem for multivalued mappings, which seem to extend and improve some well-known and celebrated results, are not correct.
A criterion for pure unrectifiability of sets (via universal vector bundle)
Let m,n be positive integers such that m < n and let G(n,m) be the Grassmann manifold of all m-dimensional subspaces of ℝⁿ. For V ∈ G(n,m) let denote the orthogonal projection from ℝⁿ onto V. The following characterization of purely unrectifiable sets holds. Let A be an -measurable subset of ℝⁿ with . Then A is purely m-unrectifiable if and only if there exists a null subset Z of the universal bundle such that, for all P ∈ A, one has . One can replace “for all P ∈ A” by “for -a.e. P ∈...
A criterion of Γ-nullness and differentiability of convex and quasiconvex functions
We introduce a criterion for a set to be Γ-null. Using it we give a shorter proof of the result that the set of points where a continuous convex function on a separable Asplund space is not Fréchet differentiable is Γ-null. Our criterion also implies a new result about Gâteaux (and Hadamard) differentiability of quasiconvex functions.
A critical point result for non-differentiable indefinite functionals
In this paper, two deformation lemmas concerning a family of indefinite, non necessarily continuously differentiable functionals are proved. A critical point theorem, which extends the classical result of Benci-Rabinowitz [14, Theorem 5.29] to the above-mentioned setting, is then deduced.
A degenerate parabolic equation in noncylindrical domains.
A derivation formula for convex integral functionals defined on .
A deterministic affine-quadratic optimal control problem
A deterministic affine-quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the optimal control is unique which leads to the differentiability of the value function. Therefore, the value function satisfies the corresponding Hamilton–Jacobi–Bellman equation in the classical sense, and the optimal control admits a state feedback representation. Under some additional...
A deterministic approach to the Skorokhod problem
A deterministic LQ tracking problem: parametrisation of the controller
The article discusses an optimal Linear Quadratic (LQ) deterministic control problem when the Youla–Kučera parametrisation of controller is used. We provide a computational procedure for computing a deterministic optimal single-input single-output (SISO) controller from any stabilising controller. This approach allows us to calculate a new optimal LQ deterministic controller from a previous one when the plant has changed. The design based on the Youla –Kučera parametrisation approach is compared...
A Differential Game Described by a Hyperbolic System
An antagonistic differential game of hyperbolic type with a separable linear vector pay-off function is considered. The main result is the description of all ε-Slater saddle points consisting of program strategies, program ε-Slater maximins and minimaxes for each ε ∈ R^N > for this game. To this purpose, the considered differential game is reduced to find the optimal program strategies of two multicriterial problems of hyperbolic type. The application...
A diffusion problem with gradient constraint and evolutive Dirichlet condition
A Direct proof for lower semicontinuity of polyconvex functionals.