Related papers: Approximations of Rockafellians, Lagrangians, and …
In practice, optimization models are often prone to unavoidable inaccuracies due to dubious assumptions and corrupted data. Traditionally, this placed special emphasis on risk-based and robust formulations, and their focus on…
In this paper, we show how approximating Rockafellians serve as a principled and effective alternative for improving the stability of stochastic programs under distributional changes. Unlike previous efforts that focus on special…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
Stochastic optimization problems are generally known to be ill-conditioned to the form of the underlying uncertainty. A framework is introduced for optimal control problems with partial differential equations as constraints that is robust…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…
We present new results on optimization problems where the involved functions are evenly convex. By means of a generalized conjugation scheme and the perturbation theory introduced by Rockafellar, we propose an alternative dual problem for a…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
We study the behaviour of solutions to a class of nonlinear degenerate parabolic problems when the data are perturbed. The class includes the Richards equation, Stefan problem and the parabolic $p$-Laplace equation. We show that, up to a…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
The recent results of An, Luan, and Yen [Differential stability in convex optimization via generalized polyhedrality. Vietnam J. Math. https://-doi.org/10.1007/s10013-024-00721-y] on differential stability of parametric optimization…
We examine the duality theory for a class of non-convex functions obtained by composing a convex function with a continuous one. Using Fenchel duality, we derive a dual problem that satisfies weak duality under general assumptions. To…