Related papers: Directional subdifferential of the value function
This paper addresses the problem of stochastic optimization with decision-dependent uncertainty, a class of problems where the probability distribution of the uncertain parameters is influenced by the decision-maker's actions. While recent…
In this paper, we revisit the Mordukhovich's subdifferential criterion for Lipschitz continuity of nonsmooth functions and coderivative criterion for the Aubin/Lipschitz-like property of set-valued mappings in finite dimensions. The…
We propose a novel family of decision-aware surrogate losses, called Perturbation Gradient (PG) losses, for the predict-then-optimize framework. The key idea is to connect the expected downstream decision loss with the directional…
Subdifferentials of a singular convex functional representing the surface free energy of a crystal under the roughening temperature are characterized. The energy functional is defined on Sobolev spaces of order -1, so the subdifferential…
Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute…
This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
The aim of this work is to provide formulae for the subdifferential and the conjungate function of the supremun function over an arbitrary family of functions. The work is principally motivated by the case when data functions are lower…
An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls…
The paper considers the problem of constructing program control for an object described by a system with a quasidifferentiable right-hand side. The control aim is to bring the system from a given initial position to a given final state in…
We consider a generalized equation governed by a strongly monotone and Lipschitz single-valued mapping and a maximally monotone set-valued mapping in a Hilbert space. We are interested in the sensitivity of solutions w.r.t. perturbations of…
The paper is devoted to the classical variational problem with a nonsmooth integrand of the functional to be minimized. The integrand is supposed to be subdifferentiable. Under some natural conditions the subdifferentiability of the…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued…
We consider a quasi-variational inequality governed by a moving set. We employ the assumption that the movement of the set has a small Lipschitz constant. Under this requirement, we show that the quasi-variational inequality has a unique…
We explore the possibility to derive basic calculus rules for some subdifferential constructions associated to set-valued maps between normed vector spaces. Then, we use these results in order to write optimality conditions for a special…
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…
In this paper we study sufficient conditions for metric subregularity of a set-valued map which is the sum of a single-valued continuous map and a locally closed subset. First we derive a sufficient condition for metric subregularity which…