Related papers: Non-Smooth Integrability Theory
We study the budget map and the indirect utility function of a parametric consumer problem in a Banach space setting by some advanced tools from set-valued and variational analysis. The Lipschitz-likeness and differentiability properties of…
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 single time-scale stochastic subgradient method for constrained optimization of a composition of several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz and differentiable in a generalized…
We obtain variants of the classical von Neumann-Morgenstern expected utility theorem, with and without the completeness axiom, in which the derived Bernoulli utility functions are Lipschitz. The prize space in these results is an arbitrary…
Slutsky symmetry and negative semidefiniteness are necessary and sufficient conditions for the rationality of demand functions. While the empirical implications of Slutsky negative semidefiniteness in repeated cross-sectional demand data…
In this paper, we prove new existence and multiplicity results for critical points of lower semicontinuous functionals in Banach spaces, complementing the nonsmooth critical point theory set forth by Szulkin and avoiding the need of the…
This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…
I explain a direct approach to differentiation and integration. Instead of relying on the general notions of real numbers, limits and continuity, we treat functions as the primary objects of our theory, and view differentiation as division…
In the present paper, a systematic study is made of quantitative semicontinuity (a.k.a. Lipschitzian) properties of certain multifunctions, which are defined as a solution map associated to a family of parameterized ``split" feasibility…
We prove a non-smooth generalization of the global implicit function theorem. More precisely we use the non-smooth local implicit function theorem and the non-smooth critical point theory in order to prove a non-smooth global implicit…
McFadden's random-utility model of multinomial choice has long been the workhorse of applied research. We establish shape-restrictions under which multinomial choice-probability functions can be rationalized via random-utility models with…
The aim of this article is to define a notion of cardinal utility function called measurable utility and to define it on a connected and separable subset of a weakly ordered topological space. The definition is equivalent to the ones given…
We establish an abstract critical point theorem for locally Lipschitz functionals that does not require any compactness condition of Palais-Smale type. It generalizes and unifies three other critical point theorems established in…
This book is devoted to finite-dimensional problems of non-convex non-smooth optimization and numerical methods for their solution. The problem of nonconvexity is studied in the book on two main models of nonconvex dependencies: these are…
We formulate conditions for the solvability of the problem of robust utility maximization from final wealth in continuous time financial markets, without assuming weak compactness of the densities of the uncertainty set, as customary in the…
We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…
Theoretical estimates of the convergence rate of many well-known gradient-type optimization methods are based on quadratic interpolation, provided that the Lipschitz condition for the gradient is satisfied. In this article we obtain a…
The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems…
Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the…
In this paper, we study the continuity of expected utility functions, and derive a necessary and sufficient condition for a weak order on the space of simple probabilities to have a continuous expected utility function. We also verify that…