相关论文: Twice epi-differentiablity and parabolic regularit…
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…
The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…
This paper is devoted to the study of the second-order variational analysis of spectral functions. It is well-known that spectral functions can be expressed as a composite function of symmetric functions and eigenvalue functions. We…
This work provides a systematic study of the variational properties of decomposable functions which are compositions of an outer support function and an inner smooth mapping under certain constraint qualifications. A particular focus is put…
Second-order variational properties have been shown to play important theoretical and numerical roles for different classes of optimization problems. Among such properties, twice epi-differentiability has a special place because of its…
In this paper, our focus lies on the study of the second-order variational analysis of orthogonally invariant matrix functions. It is well-known that an orthogonally invariant matrix function is an extended-real-value function defined on…
Deterministic two-way transducers with pebbles (aka pebble transducers) capture the class of polyregular functions, which extend the string-to-string regular functions allowing polynomial growth instead of linear growth. One of the most…
This paper mainly studies the quadratic growth and the strong metric subregularity of the subdifferential of a function that can be represented as the sum of a function twice differentiable in the extended sense and a subdifferentially…
Nonuniform exponential dichotomy serves as an important characteristic of nonuniform hyperbolicity, while admissibility of function classes is often used to characterize nonuniform exponential dichotomy. In this paper, we investigate the…
We define and study classes of smooth functions which are less regular than Gevrey functions. To that end we introduce two-parameter dependent sequences which do not satisfy Komatsu's condition (M.2)', which implies stability under…
In this paper, we introduce and investigate a class P of continuous and periodic functions on R. The class P is defined so that second-order central differences of a function satisfy some concavity-type estimate. Although this definition…
$\mathcal C^2$-partial smoothness of functions has been an important subject of research in optimization, on both theoretical and algorithmic aspects, since it was first introduced by Lewis in 2002. Our work aims at providing a fresh…
We investigate the unique solvability of second order parabolic equations in non-divergence form in $W_p^{1,2}((0,T) \times \bR^d)$, $p \ge 2$. The leading coefficients are only measurable in either one spatial variable or time and one…
In this paper we study regularity of partial differential equations with polynomial coefficients in non isotropic Beurling spaces of ultradifferentiable functions of global type. We study the action of transformations of Gabor and Wigner…
In this work there is established an optimal existence and regularity theory for second order linear parabolic differential equations on a large class of noncompact Riemannian manifolds. Then it is shown that it provides a general unifying…
Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of important classes of functions in variational analysis. Focusing mainly on the behavior of the…
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…
The paper deals with second order abstract linear partial differential equations (LPDE) over a partial differential field with two commuting differential operators. In terms of usual differential equations the main content can be presented…
Along the optimal trajectory of an optimal control problem constrained by a semilinear parabolic partial differential equation, we prove the differentiability of the value function with respect to the initial condition and, under additional…
We develop an optimal regularity theory for parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces. The results extend the classical Schauder estimates to coefficients that are merely measurable in time and…