Related papers: Bridging local and semilocal stability: A topologi…

To minimize or upper-bound the value of a function "robustly", we might instead minimize or upper-bound the "epsilon-robust regularization", defined as the map from a point to the maximum value of the function within an epsilon-radius. This…

The purpose of this paper is to make a comprehensive connection between the basic results and properties derived from the two kinds of topologies (namely the $(\epsilon,\lambda)-$topology introduced by the author and the stronger locally…

In this paper, we study Lipschitz continuity of the solution mappings of regularized least-squares problems for which the convex regularizers have (Fenchel) conjugates that are $\mathcal{C}^2$-cone reducible. Our approach, by using…

In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth…

In this paper we present a new proof of the sufficiency theorem for strong local minimizers concerning $C^1$-extremals at which the second variation is strictly positive. The results are presented in the quasiconvex setting, in accordance…

This paper investigates strong metric subregularity around a reference point as introduced by H. Gfrerer and J. V. Outrata. In the setting of Banach spaces, we analyse its stability under Lipschitz continuous perturbations and establish its…

We study proximal random reshuffling for minimizing the sum of locally Lipschitz functions and a proper lower semicontinuous convex function without assuming coercivity or the existence of limit points. The algorithmic guarantees pertaining…

We construct a local Lipschitz graph around a soliton of the cubic focusing NLS in three dimensions on which global solutions exist, and asymptotic stability as well as scattering holds.

Using techniques of variational analysis, necessary and sufficient subdifferential conditions for H\"older error bounds are investigated and some new estimates for the corresponding modulus are obtained. As an application, we consider the…

This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimizers for a broad class of…

We find conditions for a smooth nonlinear map $f:U\rightarrow V$ between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some $c$ and each positive $\varepsilon<c$ the image $% f(B_\varepsilon(x))$ of…

We establish Lipschitz regularity of harmonic maps from $\mathrm{RCD}(K,N)$ metric measure spaces with lower Ricci curvature bounds and dimension upper bounds in synthetic sense with values into $\mathrm{CAT}(0)$ metric spaces with…

In this paper, we investigate several properties of the solution maps of variational inequalities with polynomial data. First, we prove some facts on the $R_0$-property, the local boundedness, and the upper semicontinuity of the solution…

We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional…

In contrast to the usual Lipschitz seminorms associated to ordinary metrics on compact spaces, we show by examples that Lipschitz seminorms on possibly non-commutative compact spaces are usually not determined by the restriction of the…

This work considers the question: what convergence guarantees does the stochastic subgradient method have in the absence of smoothness and convexity? We prove that the stochastic subgradient method, on any semialgebraic locally Lipschitz…

This paper investigates the tilt stability of local minimizers for nonlinear programs under the relaxed constant rank constraint qualification in finite dimensions. By employing a neighborhood primal-dual approach and extending calculus…

There are several Teichm\"uller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint (a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal…

Entropic Brenier maps are regularized analogues of Brenier maps (optimal transport maps) which converge to Brenier maps as the regularization parameter shrinks. In this work, we prove quantitative stability bounds between entropic Brenier…

This paper is devoted to the analysis of a semilinear suspension bridge model with pointwise localized dissipation. The main contribution of the work is the development of a robust semigroup framework that substantially simplifies the…