Related papers: On the quantitative solution stability of paramete…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class…
We consider a parametric family of quadratically constrained quadratic programs (QCQP) and their associated semidefinite programming (SDP) relaxations. Given a nominal value of the parameter at which the SDP relaxation is exact, we study…
We study constraint satisfaction problems on the so-called 'planted' random ensemble. We show that for a certain class of problems, e.g. graph coloring, many of the properties of the usual random ensemble are quantitatively identical in the…
The paper investigates sufficient conditions on a differential inclusion which guarantee that the origin is a finite time stable equilibrium, namely a weak local one, a weak global one or a strong local one. The analysis relies on the…
Research on bias in machine learning algorithms has generally been concerned with the impact of bias on predictive accuracy. We believe that there are other factors that should also play a role in the evaluation of bias. One such factor is…
This paper delves into the challenging issues in uncertain multi-objective optimization, where uncertainty permeates nonsmooth nonconvex objective and constraint functions. In this context, we investigate highly robust (weakly efficient)…
This chapter investigates the cone of copositive matrices, with a focus on the design and analysis of conic inner approximations for it. These approximations are based on various sufficient conditions for matrix copositivity, relying on…
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…
This review paper discusses the developments in immersed or unfitted finite element methods over the past decade. The main focus is the analysis and the treatment of the adverse effects of small cut elements. We distinguish between adverse…
This article deals with the design of saturated controls in the context of partial differential equations. It focuses on a Korteweg-de Vries equation, which is a nonlinear mathematical model of waves on shallow water surfaces. Two different…
This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications…
The Balanced Stable Marriage problem is a central optimization version of the classic Stable Marriage problem. Here, the output cannot be an arbitrary stable matching, but one that balances between the dissatisfaction of the two parties,…
In this paper, we investigate well-posedness and stability properties of distributed parameter systems, with particular emphasis on linear positive control systems. We establish a characterization of the well-posedness in the Banach lattice…
This paper pursues a two-fold goal. Firstly, we aim to derive novel second-order characterizations of important robust stability properties of perturbed Karush-Kuhn-Tucker systems for a broadclass of constrained optimization problems…
Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar…
We study the optimization of the stable marriage problem. All individuals attempt to optimize their own satisfaction, subject to mutually conflicting constraints. We find that the stable solutions are generally not the globally best…
We propose a novel dynamical framework for solving inclusion problems of the form \(0 \in F(x) + G(x)\) in Hilbert spaces, where \(F\) is a maximal set-valued operator and \(G\) is a single-valued mapping. The analysis is conducted under a…
We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also…
Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…