Related papers: Implications of structured continuous maximal regu…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
We consider optimization problems with a disjunctive structure of the constraints. Prominent examples of such problems are mathematical programs with equilibrium constraints or vanishing constraints. Based on the concepts of directional…
We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show that solutions to the Yamabe flow instantaneously regularize…
We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider…
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…
We give a short, simple proof of maximal regularity for linear parabolic evolution equations on manifolds with cylindrical ends by making use of pseudodifferential parametrices and the concept of R-boundedness for the resolvent.
The use of min-max optimization in adversarial training of deep neural network classifiers and training of generative adversarial networks has motivated the study of nonconvex-nonconcave optimization objectives, which frequently arise in…
Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…
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…
We characterize order preserving continuous surjections between compact linearly ordered spaces which admit an averaging operator, together with estimates of the norm of such an operator. This result is used to the study of strengthenings…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
This paper studies smoothing properties of the local fractional maximal operator, which is defined in a proper subdomain of the Euclidean space. We prove new pointwise estimates for the weak gradient of the maximal function, which imply…
We establish higher regularity properties of solutions to fully nonlinear elliptic equations at interior critical points. The key novelty of our estimates lies in the fact that they yield smoothness properties that go beyond the inherent…
Estimating the regular normal cone to constraint systems plays an important role for the derivation of sharp necessary optimality conditions. We present two novel approaches and introduce a new stationarity concept which is stronger than…
In this manuscript we study geometric regularity estimates for problems driven by fully nonlinear elliptic operators under strong absorption conditions. We establish improved geometric regularity along the free boundary, for a sharp value…
We consider distributions on a closed compact manifold $M$ as maps on smoothing operators. Thus spaces of certain maps between $\Psi^{-\infty}(M)\to \mathcal{C}^{\infty}(M)$ are considered as generalized functions. For any collection of…
We study various regularization operators on plurisubharmonic functions that preserve Lelong classes with growth given by certain compact convex sets. The purpose is to show that the weighted Siciak-Zakharyuta functions associated with…
In this paper, we investigate in a unified way the structural properties of solutions to inverse problems. These solutions are regularized by the generic class of semi-norms defined as a decomposable norm composed with a linear operator,…