9 papers
Random multifunctions as the set minimizers of infinitely many differentiable random functions
Juan Guillermo Garrido, Pedro Pérez-Aros, Emilio Vilches
Under mild assumptions, we prove that any random multifunction can be represented as the set of minimizers of an infinitely many differentiable normal integrand, which preserves th…
Generalized Leibniz rules and Lipschitzian stability for expected-integral mappings
Boris S. Mordukhovich, Pedro Pérez-Aros
This paper is devoted to the study of the expected-integral multifunctions given in the form \begin{equation*} \operatorname{E}_Φ(x):=\int_TΦ_t(x)dμ, \end{equation*} where $Φ\colon…
New extremal principles with applications to stochastic and semi-infinite programming
Boris S. Mordukhovich, Pedro Pérez-Aros
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programmi…
Tikhonov-like regularization of dynamical systems associated with nonexpansive operators defined in closed and convex sets
Pedro Pérez-Aros, Emilio Vilches
In this paper, we propose a Tikhonov-like regularization for dynamical systems associated with non-expansive operators defined in closed and convex sets of a Hilbert space. We prov…
An enhanced Baillon-Haddad theorem for convex functions on convex sets
Pedro Pérez-Aros, Emilio Vilches
The Baillon-Haddad theorem establishes that the gradient of a convex and continuously differentiable function defined in a Hilbert space is -Lipschitz if and only if it is …
Ergodic Approach to Robust Optimization and Infinite Programming Problems
Pedro Pérez-Aros
In this work, we show the consistency of an approach for solving robust optimization problems using sequences of sub-problems generated by ergodic measure preserving transformation…