Related papers: On Differential Stability of a Class of Convex Opt…
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…
The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of…
When computing bounds, spatial branch-and-bound algorithms often linearly outer approximate convex relaxations for non-convex expressions in order to capitalize on the efficiency and robustness of linear programming solvers. Considering…
Generalized polyhedral convex sets, generalized polyhedral convex functions on locally convex Hausdorff topological vector spaces, and the related constructions such as sum of sets, sum of functions, directional derivative, infimal…
Recently, based on the idea of randomizing space theory, random convex analysis has been being developed in order to deal with the corresponding problems in random environments such as analysis of conditional convex risk measures and the…
This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…
The paper introduces and characterizes new notions of Lipschitzian and H\"olderian full stability of solutions to general parametric variational systems described via partial subdifferential and normal cone mappings acting in Hilbert…
The paper presents methods of eigenvalue localisation of regular matrix polynomials, in particular, stability of matrix polynomials is investigated. For this aim a stronger notion of hyperstability is introduced and widely discussed. Matrix…
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…
This paper establishes several new facts on generalized polyhedral convex sets and shows how they can be used in vector optimization. Among other things, a scalarization formula for the efficient solution sets of generalized vector…
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…
In this paper, we investigate the continuous time partial primal-dual gradient dynamics (P-PDGD) for solving convex optimization problems with the form $ \min\limits_{x\in X,y\in\Omega}\ f({x})+h(y),\ \textit{s.t.}\ A{x}+By=C $, where $…
Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
We prove that uniform second order growth, tilt stability, and strong metric regularity of the limiting subdifferential --- three notions that have appeared in entirely different settings --- are all essentially equivalent for any…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
This paper focuses on the stability of both local and global error bounds for a proper lower semicontinuous convex function defined on a Banach space. Without relying on any dual space information, we first provide precise estimates of…
The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…
We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
In this work, we study the external and internal stability of minimal solutions to set-valued optimization problems in a new functional framework. We consider perturbations on both the objective function and the admissible domain. To…