Related papers: Variational inequalities characterizing weak minim…

In this article we introduce a definition of topological minimal sets, which is a generalization of that of Mumford-Shah-minimal sets. We prove some general properties as well as two existence theorems for topological minimal sets. As an…

The paper is devoted to the existence of global optimal solutions for a general class of nonsmooth problems of constrained vector optimization without boundedness assumptions on constraint sets. The main attention is paid to the two major…

(English) This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in $\mathbb{R}^k$. In some places, a more general formulation in metric spaces is provided. It lays out the necessary…

Using an alternative notion of entropy introduced by Datta, the max-entropy, we present a new simplified framework to study the minimizers of the specific free energy for random fields which are weakly dependent in the sense of Lewis,…

We formulate a notion of "geometric reductivity" in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that the ring of invariants is finitely generated. This result…

This paper focuses on optimization problems constrained by Parametric Variational Inequalities (PVI) defined on a moving set. Unlike most existing works on mathematical programs with equilibrium constraints, the equilibrium constraints have…

Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this…

We derive and analyse a boundary element formulation for boundary conditions involving inequalities. In particular, we focus on Signorini contact conditions. The Calder\'on projector is used for the system matrix and boundary conditions are…

We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.

We study minimum entropy submodular optimization, a common generalization of the minimum entropy set cover problem, studied earlier by Cardinal et al., and the submodular set cover problem. We give a general bound of the approximation…

This paper exemplifies that saturation is an indispensable structure on measure spaces to obtain the existence and characterization of solutions to nonconvex variational problems with integral constraints in Banach spaces and their dual…

Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…

Lower semi-continuity (\texttt{LSC}) is a critical assumption in many foundational optimisation theory results; however, in many cases, \texttt{LSC} is stronger than necessary. This has led to the introduction of numerous weaker continuity…

The (extensional) theory of arrays is widely used to model systems. Hence, efficient decision procedures are needed to model check such systems. Current decision procedures for the theory of arrays saturate the read-over-write and…

In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions objects are…

Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…

In recent developments, a novel set of necessary optimality conditions for mixed constrained optimal control problems, termed the asymptotic weak maximum principle, has been formulated. These novel conditions deviate from the classical ones…

We present a sufficient condition that a pseudointegrable system has weak mixing property. The result is derived from Veech's weak mixing theorem for interval exhange [Veech, W.A. Amer.J.Math. {\bf 106}, 1331 (1984)]. We also present an…

We prove the existence of weak solutions for distribution-dependent stochastic Volterra equations under linear growth and continuity conditions on the coefficients and mild regularity assumptions on the kernels, including singular kernels.…

Ren and the second author established that the weakly optimal subvarieties (e.g. maximal weakly special subvarieties) of a subvariety $V$ of a Shimura variety arise in finitely many families. In this article, we refine this theorem by (1)…