In many applications, one deals with nonsmooth functions, e.g., in dynamical systems, mechanics, or optimization. order to establish theoretical results, it is often beneficial regularize the functions an intermediate step. this work, we investigate properties of a generalization Moreau–Yosida regularization on normed space where replace quadratic kernel infimal convolution more general functio...

In this paper, we consider the Lagrangian dual problem of a class of convex optimization problems. We first discuss the semismoothness of the Lagrangian-dual function φ. This property is then used to investigate the second-order properties of the Moreau-Yosida regularization η of the function φ, e.g., the semismoothness of the gradient g of the regularized function η. We show that φ and g are p...

Several results are proved concerning representations of multiplier algebras that arise as extensions of representations of underlying Banach algebras. These results are then used to rederive Kisyński’s generalisation of the Hille–Yosida theorem and to establish two generalisations of the Trotter–Kato theorem, one of which, involving Banach bundles, is abstract and the other is classical in cha...

In this paper, we introduce and study degenerate state-dependent sweeping processes with nonregular moving sets (subsmooth positively $$\alpha $$ -far). Based on the Moreau–Yosida regularization, prove existence of solutions under Lipschitzianity respect to truncated Hausdorff distance.

In analysis, truncation is the operation of replacing a nonnegative real-valued function a (x) by its pointwise meet a (x) ∧ 1 with the constant 1 function. A vector lattice A is said to be closed under truncation if a ∧ 1 ∈ A for all a ∈ A. Note that A need not contain 1 itself. Truncation is fundamental to analysis. To give only one example, Lebesgue integration generalizes beautifully to any...

We consider a formulation of the Maxwell system which involves pseudo-differential operators in time. This formulation has been analyzed in a previous work and it has been proved that it is a Perfectly Matched Layer model for electromagnetic waves propagating into the vacuum. We establish that the system admits a single solution by adapting the Hille-Yosida theory.