Related papers: Metric Regularity of Quasidifferentiable Mappings …
This paper presents a unified derivation of transversality conditions in optimal control problems using exact penalty functions. The key regularity condition is that the origin is uniformly separated from the subdifferential of the penalty…
We employ a fuzzy optimality condition for the Frechet subdifferential and some advanced techniques of variational analysis such as formulae for the subdifferentials of an infinite family of nonsmooth functions and the coderivative…
The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems:…
We establish uniformization results for metric spaces that are homeomorphic to the euclidean plane or sphere and have locally finite Hausdorff 2-measure. Applying the geometric definition of quasiconformality, we give a necessary and…
Optimization problems with constraints in the form of a partial differential equation arise frequently in the process of engineering design. The discretization of PDE-constrained optimization problems results in large-scale linear systems…
In this paper, we develop the foundations of the theory of quasiregular mappings in general metric measure spaces. In particular, nine definitions of quasiregularity for a discrete open mapping with locally bounded multiplicity are proved…
In this note, we give an introduction to the concept of maximal $L^p$-regularity as a method to solve nonlinear partial differential equations. We first define maximal regularity for autonomous and non-autonomous problems and describe the…
In the past years, the phenomenon of fractional regularity has been addressed for a large class of linear and/or quasilinear differential operators, mostly, in terms of certain Besov spaces. As it turned out, for equations governed by the…
We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…
The paper studies generalized differentiability properties of the marginal function of parametric optimal control problems of semilinear elliptic partial differential equations. We establish upper estimates for the regular and the limiting…
The main purpose of this paper is to investigate the properties of a mapping which is required to be roughly bilipschitz with respect to the Apollonian metric (roughly Apollonian bilipschitz) of its domain. We prove that under these…
This paper is concerned with an optimal control problem governed by nonsmooth semilinear elliptic partial differential equations with both distributed and boundary unilateral pointwise control constraints, in which the nonlinear coefficient…
We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mappings of bounded multiplicity is quasi-nearly subharmonic. Also, we prove that if $u\circ f$ is quasi-nearly subharmonic for all quasi-nearly…
We consider the problem of extraction and validation of matching rules, directly from the phased diffraction data of a quasicrystal, and propose an algorithmic procedure to produce the rules of the shortest possible range. We have developed…
We propose a unified framework for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching…
This paper showcases the effectiveness of the quasiconvexity property in addressing the optimal regularity of the temporal derivative and establishes conditions for its continuity in nonlocal time-dependent obstacle problems.
Mathematical Program with Complementarity Constraints (MPCC) plays a very important role in many fields such as engineering design, economic equilibrium, multilevel game, and mathematical programming theory itself. In theory its constraints…
This paper considers the problem of minimizing the summation of a differentiable function and a nonsmooth function on a Riemannian manifold. In recent years, proximal gradient method and its invariants have been generalized to the…
We develop a new method suitable for establishing lower bounds on the ball measure of noncompactness of operators acting between considerably general quasinormed function spaces. This new method removes some of the restrictions…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…