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On Hadamard-Type Inequalities for Co--ordinated r-Convex Functions
r− Convex Hadamard-Type Inequalities Co–ordinates
2010/12/9
In this paper we defined r−convexity on the coordinates and we established some Hadamard-Type Inequalities.
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...
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...
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...
Turnpike Theorem for Convex Infinite Dimensional Discrete-Time Control Systems
Turnpike property Banach space convex function generic function
2009/1/23
In this work we study the structure of "approximate" solutions for an infinite dimensional discrete-time optimal control problem determined by a convex function $v: K \times K \to R^1$, where $K$ is a...
Limiting Convex Examples for Nonconvex Subdifferential Calculus
Nonsmooth analysis subdifferentials coderivatives extremal principle open mapping theorem metric regularity multiplier rules compactly Lipschitzian conditions
2009/1/23
We show, largely using convex examples, that most of the core results for limiting subdifferential calculus fail without additional restrictions in infinite dimensional Banach spaces.
Vertical Developments of a Convex Function
Convex analysis second-order derivative approximate subdifferential semidefinite programming
2009/1/22
In this paper we compare two different approaches to analyse the second-order behaviour of a convex function. The first one is classical, we call it the horizontal approach; the second one is more rec...
The Barrier Cone of a Convex Set and the Closure of the Cover
convex set barrier cone recession cone cover polar cone
2009/1/22
For an arbitrary non-empty closed convex set $A$ in $\mathbb{R}^n$, we prove that the polar of the difference between the barrier cone $\mathbb{B}(A)$ and its interior $\text{int } \mathbb{B} (A)$ co...
A Note on the Closedness of the Convex Hull and Its Applications
Convex Hull Applications spannability
2009/1/22
This paper answers the following question motivated by the problem of spannability of functions. When is the convex hull of an unbounded (closed) set closed? We provide necessary and sufficient condit...
Invariants of Pairs of Compact Convex Sets
Pairs of convex sets sublinear function quasidifferential calculus
2009/1/22
In a recent paper P. Diamond, P. Kloeden, A. Rubinov and A. Vladimirov [3] investigated comperative properties of three different metrics in the space of pairs of compact convex sets. These metrics de...
On a Non-Standard Convex Regularization and the Relaxation of Unbounded Integral Functionals of the Calculus of Variations
Non-Standard Convex Regularization Integral Functionals Calculus of Variations
2009/1/20
The analysis of the relationships between the functional $F^{(\infty)}(\Omega,\cdot) \colon u \in W^{1,\infty}(\Omega) \mapsto \inf$ $\{\liminf_h \int_\Omega f(\nabla u_h)dx : \{u_h\}$ $\subseteq W^{1...
Least Deviation Decomposition with Respect to a Pair of Convex Sets
Least deviation decomposition convex analysis Moreau orthogonal decomposition
2009/1/20
Let $K_1$ and $K_2$ be two nonempty closed convex sets in some normed space $(H,\Vert \cdot \Vert )$. This paper is concerned with the question of finding a "good" decomposition, with respect to $K_1$...