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Geometric Approximation of Proximal Normals
Nonsmooth analysis distance function $\delta$-projection proximal normal proximal subdifferential
2009/2/5
For $x\in H\setminus S$ and $\delta \ge 0$, the $\delta$-projection of $x$ onto $S$, is the set $\operatorname{proj}_S^\delta(x):=\left\{s\in S \colon \|s-x\|^2 \le d_S(x)^2 + \delta^2 \right\}.$ We p...
On the Structure of Nash Equilibrium Sets in Partially Convex Games
Nash Equilibrium Partially Convex Games
2009/2/5
The paper describes the geometrical structure of Nash equilibrium sets in partially convex games without constraints. A condition characterizing a distinct class of Nash equilibrium sets is given. A c...
Are Some Optimal Shape Problems Convex?
optimal shape plate equation convexity maximal deformation beam
2009/2/5
The optimal shape problem in this paper is to construct plates or beams of minimal weight. The thickness $u(x)$ is variable, but the vertical deformation $y(x)$ should not exceed a certain threshhold....
Shape Optimization Problems over Classes of Convex Domains
Shape Optimization Problems Convex Domains
2009/2/5
We consider shape optimization problems of the form
\min\left\{\int_{\partial A} f(x,\nu(x))\hbox{d}x {\cal{H}^{n-1}} :A\in{\cal A}\right\}
where $f$ is any continuous function and the class ${\ca...
Decompositions of Compact Convex Sets
Pairs of convex sets sublinear function quasidifferential calculus
2009/2/5
In a recent paper R. Urbanski [13] investigated the mimimality of pairs compact convex sets which satisfy additional conditions, namely the minimal convex pairs. In this paper we consider some differe...
An Elementary Proof of Komlos-Révész Theorem in Hilbert Spaces
Convergence Hilbert space Komlos Révész
2009/2/5
We provide an elementary proof of Komlos-Révész theorem in Hilbert spaces.
Rank-one-convex and Quasiconvex Envelopes for Functions Depending on Quadratic Forms
rank-one-convex quasiconvex envelope quadratic form James-Ericksen function Pipkin's formula
2009/2/5
In this paper we are interested in functions defined, on a set of matrices, by the mean of quadratic forms and we compute the rank-one-convex, quasiconvex, polyconvex and convex envelopes of these fun...
BMO Regularity for One-Dimensional Minimizers of some Lagrange Problems
Calculus of Variations One-dimensional problems Reverse Jensen Inequalities Tonelli set $BMO$ Orlicz Spaces
2009/2/5
We extend our results about a class of non-regular Lagrange problems of Calculus of Variations showing that the derivative of minimizers are in $BMO$. For this class we give also some results of optim...
A Generalization of the Quasiconvex Optimization Problem
Quasiconvex Optimization Problem instead of functions convex minimization problem
2009/2/5
In this paper the quasiconvex minimization problem is included in a problem defined by sets (instead of functions). Lagrangian conditions for both problems are then studied and related. Lagrangian con...
Existence of Regular Solutions for a One-Dimensional Simplified Perfect-Plastic Problem with a Unilateral Gradient Constraint
Regular Solutions Unilateral Gradient Constraint One-Dimensional Simplified Perfect-Plastic Problem
2009/2/5
This work is devoted to the study of the existence of "regular" solutions for a one-dimensional problem with unilateral constrained gradient in Perfect-Plasticity.
The particularity of this problem ...
Minimization of Nonsmooth Convex Functionals in Banach Spaces
Banach spaces nonsmooth optimization subgradient methods metric projection generalized projection weak convergence
2009/2/5
We develop a unified framework for convergence analysis of subgradient and subgradient projection methods for minimization of nonsmooth convex functionals in Banach spaces. The important novel featu...
Proto-Derivatives of Partial Subgradient Mappings
Variational analysis subgradient mappings proto-derivatives second-order epi-derivatives amenable functions piecewise-$C^2$ functions nonsmooth analysis
2009/2/5
Partial subgradient mappings have a key role in the sensitivity analysis of first-order conditions for optimality, and their generalized derivatives are especially important in that respect. It is k...
Complements, Approximations, Smoothings and Invariance Properties
Nonsmooth analysis epi-Lipschitz complement approximations invariance differential inclusion smoothing proximal smoothness ]tangentiality feedback convolution Hamiltonian-Jacobi inequalities
2009/2/5
Proximal methods are used to determine the relationship between normal cones to a closed set in $\Re^n$ and those to the closure of its complement. The geometry of outer and inner set approximations i...
(Positively) homogeneous functions play a special role in the Legendre-Fenchel duality. The Legendre-Fenchel conjugate of a $p$-homogeneous function is a $q$-homogeneous function with $1/p+1/q=1$. Fu...
A Viability Result in the Upper Semicontinuous Case
Viability Result Upper Semicontinuous Case $u'\in F(t,u)$
2009/1/23
We prove the existence of solutions of a differential inclusion $u'\in F(t,u)$ in a separable Banach space $X$ with constraint $u(t)\in D(t)$. $F$ is globally measurable, weakly upper semicontinuous w...