254 research outputs found
Density of convex intersections and applications
In this paper we address density properties of intersections of convex sets in several
function spaces. Using the concept of Gamma-convergence, it is shown in a general framework,
how these density issues naturally arise from the regularization, discretization or dualization
of constrained optimization problems and from perturbed variational inequalities. A variety of
density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented
and the corresponding regularity requirements on the upper bound are identified. The results
are further discussed in the context of finite element discretizations of sets associated to convex
constraints. Finally, two applications are provided, which include elasto-plasticity and image
restoration problems
Density of convex intersections and applications
In this paper we address density properties of intersections of convex sets in several
function spaces. Using the concept of Gamma-convergence, it is shown in a general framework,
how these density issues naturally arise from the regularization, discretization or dualization
of constrained optimization problems and from perturbed variational inequalities. A variety of
density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented
and the corresponding regularity requirements on the upper bound are identified. The results
are further discussed in the context of finite element discretizations of sets associated to convex
constraints. Finally, two applications are provided, which include elasto-plasticity and image
restoration problems
Error Estimates and Lipschitz Constants for Best Approximation in Continuous Function Spaces
We use a structural characterization of the metric projection PG(f), from the continuous function space to its one-dimensional subspace G, to derive a lower bound of the Hausdorff strong unicity constant (or weak sharp minimum constant) for PG and then show this lower bound can be attained. Then the exact value of Lipschitz constant for PG is computed. The process is a quantitative analysis based on the Gâteaux derivative of PG, a representation of local Lipschitz constants, the equivalence of local and global Lipschitz constants for lower semicontinuous mappings, and construction of functions
Density of convex intersections and applications
In this paper we address density properties of intersections of convex sets in several function spaces. Using the concept of Gamma-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite element discretizations of sets associated to convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems
Density of convex intersections and applications
In this paper, we address density properties of intersections of convex sets in several function spaces. Using the concept of Γ-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite-element discretizations of sets associated with convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems
Density of convex intersections and applications
In this paper we address density properties of intersections of convex sets in several function spaces. Using the concept of Gamma-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite element discretizations of sets associated to convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems
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