Pedro Pérez-Aros
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View article: Randomized block proximal method with locally Lipschitz continuous gradient
Randomized block proximal method with locally Lipschitz continuous gradient Open
Block-coordinate algorithms are recognized to furnish efficient iterative schemes for addressing large-scale problems, especially when the computation of full derivatives entails substantial memory requirements and computational efforts. I…
View article: A Projected Variable Smoothing for Weakly Convex Optimization and Supremum Functions
A Projected Variable Smoothing for Weakly Convex Optimization and Supremum Functions Open
In this paper, we address two main topics. First, we study the problem of minimizing the sum of a smooth function and the composition of a weakly convex function with a linear operator on a closed vector subspace. For this problem, we prop…
View article: A Newton-Like Dynamical System for Nonsmooth and Nonconvex Optimization
A Newton-Like Dynamical System for Nonsmooth and Nonconvex Optimization Open
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 classi…
View article: Differentiability and Approximation of Probability Functions under Gaussian Mixture Models: A Bayesian Approach
Differentiability and Approximation of Probability Functions under Gaussian Mixture Models: A Bayesian Approach Open
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture m…
View article: Numerical solution of an optimal control problem with probabilistic and almost sure state constraints
Numerical solution of an optimal control problem with probabilistic and almost sure state constraints Open
We consider the optimal control of a PDE with random source term subject to probabilistic or almost sure state constraints. In the main theoretical result, we provide an exact formula for the Clarke subdifferential of the probability funct…
View article: The Boosted Double-Proximal Subgradient Algorithm for Nonconvex Optimization
The Boosted Double-Proximal Subgradient Algorithm for Nonconvex Optimization Open
In this paper we introduce the Boosted Double-proximal Subgradient Algorithm (BDSA), a novel splitting algorithm designed to address general structured nonsmooth and nonconvex mathematical programs expressed as sums and differences of comp…
View article: Galerkin-like Method for Integro-Differential Inclusions with applications to Volterra Sweeping processes
Galerkin-like Method for Integro-Differential Inclusions with applications to Volterra Sweeping processes Open
In this paper, we develop the Galerkin-like method to address first-order integro-differential inclusions. Under compactness or monotonicity conditions, we obtain new results for the existence of solutions for this class of problems, which…
View article: Probability functions generated by set-valued mappings: a study of first order information
Probability functions generated by set-valued mappings: a study of first order information Open
Probability functions appear in constraints of many optimization problems in practice and have become quite popular. Understanding their first-order properties has proven useful, not only theoretically but also in implementable algorithms,…
View article: Inner Moreau envelope of nonsmooth conic chance constrained optimization problems
Inner Moreau envelope of nonsmooth conic chance constrained optimization problems Open
Optimization problems with uncertainty in the constraints occur in many applications. Particularly, probability functions present a natural form to deal with this situation. Nevertheless, in some cases, the resulting probability functions …
View article: Coderivative-Based Semi-Newton Method in Nonsmooth Difference Programming
Coderivative-Based Semi-Newton Method in Nonsmooth Difference Programming Open
This paper addresses the study of a new class of nonsmooth optimization problems, where the objective is represented as a difference of two generally nonconvex functions. We propose and develop a novel Newton-type algorithm to solving such…
View article: Control in Probability for SDE Models of Growth Population
Control in Probability for SDE Models of Growth Population Open
View article: Integral functionals on nonseparable Banach spaces with applications
Integral functionals on nonseparable Banach spaces with applications Open
In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results. T…
View article: Optimality conditions in DC constrained mathematical programming problems
Optimality conditions in DC constrained mathematical programming problems Open
This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of …
View article: Sensitivity Analysis of Stochastic Constraint and Variational Systems via Generalized Differentiation
Sensitivity Analysis of Stochastic Constraint and Variational Systems via Generalized Differentiation Open
This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzia…
View article: Gradient formulae for probability functions depending on a heterogenous family of constraints
Gradient formulae for probability functions depending on a heterogenous family of constraints Open
Probability functions measure the degree of satisfaction of certain constraints that are impacted by decisions and uncertainty. Such functions appear in probability or chance constraints ensuring that the degree of satisfaction is sufficie…
View article: Random multifunctions as the set minimizers of infinitely many differentiable random functions
Random multifunctions as the set minimizers of infinitely many differentiable random functions Open
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 the convexity of the random multifunction. We provide several…
View article: Generalized Sequential Differential Calculus for Expected-Integral Functionals
Generalized Sequential Differential Calculus for Expected-Integral Functionals Open
View article: Generalized Differentiation of Expected-Integral Mappings with Applications to Stochastic Programming, II: Leibniz Rules and Lipschitz Stability
Generalized Differentiation of Expected-Integral Mappings with Applications to Stochastic Programming, II: Leibniz Rules and Lipschitz Stability Open
This paper is devoted to the study of the expected-integral multifunctions given in the form \begin{equation*} \operatorname{E}_\Phi(x):=\int_T\Phi_t(x)d\mu, \end{equation*} where $\Phi\colon T\times\mathbb{R}^n \rightrightarrows \mathbb{R…
View article: Generalized Leibniz rules and Lipschitzian stability for expected-integral mappings
Generalized Leibniz rules and Lipschitzian stability for expected-integral mappings Open
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 $Φ\colon T\times\mathbb{R}^n \rightrightarrows \mathbb{R}^m$ is a s…
View article: Ergodic Approach to Robust Optimization and Infinite Programming Problems
Ergodic Approach to Robust Optimization and Infinite Programming Problems Open
View article: New extremal principles with applications to stochastic and semi-infinite programming
New extremal principles with applications to stochastic and semi-infinite programming Open
View article: New extremal principles with applications to stochastic and\n semi-infinite programming
New extremal principles with applications to stochastic and\n semi-infinite programming Open
This paper develops new extremal principles of variational analysis that are\nmotivated by applications to constrained problems of stochastic programming and\nsemi-infinite programming without smoothness and/or convexity assumptions.\nThes…
View article: Qualification Conditions-Free Characterizations of the $$\varepsilon $$-Subdifferential of Convex Integral Functions
Qualification Conditions-Free Characterizations of the $$\varepsilon $$-Subdifferential of Convex Integral Functions Open
View article: Tikhonov-like regularization of dynamical systems associated with nonexpansive operators defined in closed and convex sets
Tikhonov-like regularization of dynamical systems associated with nonexpansive operators defined in closed and convex sets Open
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 prove the well-posedness and the strong convergence of the prop…
View article: An enhanced Baillon-Haddad theorem for convex functions on convex sets
An enhanced Baillon-Haddad theorem for convex functions on convex sets Open
The Baillon-Haddad theorem establishes that the gradient of a convex and continuously differentiable function defined in a Hilbert space is $β$-Lipschitz if and only if it is $1/β$-cocoercive. In this paper, we extend this theorem to Gâtea…
View article: Ergodic Approach to Robust Optimization and Infinite Programming\n Problems
Ergodic Approach to Robust Optimization and Infinite Programming\n Problems Open
In this work, we show the consistency of an approach for solving robust\noptimization problems using sequences of sub-problems generated by ergodic\nmeasure preserving transformations.\n The main result of this paper is that the minimizers…
View article: Ergodic Approach for Nonconvex Robust Optimization Problems
Ergodic Approach for Nonconvex Robust Optimization Problems Open
View article: Subdifferential Formulae for the Supremum of an Arbitrary Family of Functions
Subdifferential Formulae for the Supremum of an Arbitrary Family of Functions Open
This work provides calculus for the Fréchet and limiting subdifferential of the pointwise supremum given by an arbitrary family of lower semicontinuous functions. We start our study showing fuzzy results about the Fréchet subdifferential o…
View article: Characterizations of the subdifferential of convex integral functions under qualification conditions
Characterizations of the subdifferential of convex integral functions under qualification conditions Open
This work provides formulae for the $ε$-subdifferential of integral functions in the framework of complete $σ$-finite measure spaces and locally convex spaces. In this work we present here new formulae for this $ε$-subdifferential under th…
View article: Complete characterizations of the subdifferential of convex integral functions II: Qualification conditions, conjugate and sequential formulae
Complete characterizations of the subdifferential of convex integral functions II: Qualification conditions, conjugate and sequential formulae Open
This work provides formulae for the $\epsilon$-subdifferential of the integral functional given by the following expression \begin{equation*}
I_f (x):=\int\limits_T f(t,x) d\mu(t) \end{equation*} where $(T,\Sigma,\mu)$ is a complete $\si…