Related papers: Stability analysis for set-valued optimization in …
In this paper, we consider the problem of Gaussian process (GP) optimization with an added robustness requirement: The returned point may be perturbed by an adversary, and we require the function value to remain as high as possible even…
Various classes of stable finite difference schemes can be constructed to obtain a numerical solution. It is important to select among all stable schemes such a scheme that is optimal in terms of certain additional criteria. In this study,…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
We study how maximal regularity estimates with respect to the continuous functions improve automatically in cases where the spatial norm is fundamentally different from the supremum norm. More precisely, we invoke properties such as weak…
Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for…
We consider sensitivity of a semidefinite program under perturbations in the case that the primal problem is strictly feasible and the dual problem is weakly feasible. When the coefficient matrices are perturbed, the optimal values can…
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…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…
Adaptive optimal control using value iteration (VI) initiated from a stabilizing policy is theoretically analyzed in various aspects including the continuity of the result, the stability of the system operated using any single/constant…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
Improperly efficient solutions in the sense of Geoffrion in linear fractional vector optimization problems with unbounded constraint sets are studied in this paper. We give two sets of conditions which assure that all the efficient…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
Stochastic bilevel optimization (SBO) has been integrated into many machine learning paradigms recently, including hyperparameter optimization, meta learning, and reinforcement learning. Along with the wide range of applications, there have…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from…
This paper is devoted to the theoretical study of the efficiency, namely, stability of some greedy algorithms. In the greedy approximation theory researchers are mostly interested in the following two important properties of an algorithm --…