# David SalasUniversidad de O'Higgins · Instituto de Ciencias de la Ingeniería

David Salas

PhD

## About

42

Publications

4,107

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203

Citations

Introduction

Education

September 2013 - December 2016

## Publications

Publications (42)

The norm of the gradient ∇f (x) measures the maximum descent of a real-valued smooth function f at x. For (nonsmooth) convex functions, this is expressed by the distance dist(0, ∂f (x)) of the subdifferential to the origin, while for general real-valued functions defined on metric spaces by the notion of metric slope |∇f |(x). In this work we propo...

A classical result of variational analysis, known as Attouch theorem, establishes an equivalence between epigraphical convergence of a sequence of proper convex lower semicontinuous functions and graphical convergence of the corresponding subdifferential maps up to a normalization condition which fixes the integration constant. In this work, we sho...

We study linear bilevel programming problems whose lower-level objective is given by a random cost vector with known distribution. We consider the case where this distribution is nonatomic, allowing to reformulate the problem of the leader using the Bayesian approach in the sense of Salas and Svensson (SIAM J Optim 33(3):2311–2340, 2023), with a de...

In 1996, Mallozzi and Morgan [Hierarchical Systems with Weighted Reaction Set, Springer, Boston, 1996, pp. 271-282] proposed a new model for Stackelberg games which we refer to here to as the Bayesian approach. The leader has only partial information about how followers select their reaction among possibly multiple optimal ones. This partial inform...

The local slope operator was introduced in De Giorgi et al. (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Nat 68:180–187, 1980) to study gradient flow dynamics in metric spaces. This tool has now become a cornerstone in metric evolution equations (see, e.g., Ambrosio et al. (Gradient flows in metric spaces and in the space of probability measures, Lec...

We establish existence of steepest descent curves emanating from almost every point of a regular locally Lipschitz quasiconvex functions, where regularity means that the sweeping process flow induced by the sublevel sets is reversible. We then use max-convolution to regularize general quasiconvex functions and obtain a result of the same nature in...

Ride-hailing platforms typically classify drivers as either employees or independent contractors. These classifications tend to emphasize either wage certainty or flexibility, but rarely both. We study an alternative or complementary approach: the \textit{Idle wage,} which provides with a fixed payment drivers even when they are connected without p...

This work explores bilevel problems in the context of cardinality constraints. More specifically Single-Leader-Multi-Follower games (SLMFG) involving cardinality constraints are considered in two different configurations: one with the cardinality constraint at the leader's level and a mixed structure in which the cardinality constraint is split bet...

A classical result of variational analysis, known as Attouch theorem, establishes the equivalence between epigraphical convergence of a sequence of proper convex lower semicon-tinuous functions and graphical convergence of the corresponding subdifferential maps up to a normalization condition which fixes the integration constant. In this work, we s...

For drivers in ride-hailing companies, allocation within the city is paramount to get matched with rides. This decision depends on many factors, where some of them (such as demand and allocation of others) are unknown for the drivers, but are available for the company. In this work, we investigate whether it is beneficial or not for the ride-hailin...

We establish existence of steepest descent curves emanating from almost every point of a regular locally Lipschitz quasiconvex functions, where regularity means that the sweeping process induced by the sublevel sets is reversible. We then use max-convolution to regularize general quasiconvex functions and obtain a result of the same nature in a mor...

It was established in [8] that Lipschitz inf-compact functions are uniquely determined by their local slope and critical values. Compactness played a paramount role in this result, ensuring in particular the existence of critical points. We hereby emancipate from this restriction and establish a determination result for merely bounded from below fu...

We study linear bilevel programming problems whose lower-level objective is given by a random cost vector with known distribution. We consider the case where this distribution is nonatomic, allowing to pose the problem of the leader using vertex-supported beliefs in the sense of [29]. We prove that, under suitable assumptions, this formulation turn...

The norm of the gradient $\nabla$f (x) measures the maximum descent of a real-valued smooth function f at x. For (nonsmooth) convex functions, this is expressed by the distance dist(0, $\partial$f (x)) of the subdifferential to the origin, while for general real-valued functions defined on metric spaces by the notion of metric slope |$\nabla$f |(x)...

We study a bilevel programming problem with linear data, whose lower-level objective is a random variable with a known distribution. We consider the case where this distribution is nonatomic, allowing to pose the problem of the leader as the optimization of his expected value. We prove that under suitable assumptions this formulation turns out to b...

Industrial water conservation is an important adaptation to preserve the environment. Eco-Industrial Parks (EIPs) have been designed to encourage the establishment of water exchange networks between enterprises in order to minimize freshwater consumption and wastewater discharge by maximizing wastewater reuse. This control-input model presents a ma...

For drivers in ride-hailing companies, allocation within the city is paramount to get matched with rides. This decision depends on many factors, where some of them (such as demand and allocation of others) are unknown for the drivers, but are available for the company. In this work, we investigate whether it is beneficial or not for the ride-hailin...

In 1996, Mallozzi and Morgan [31] proposed a new model for bilevel games with one leader (which they called Intermediate). The leader has only partial information about how followers select their response among possible multiple optimal ones. This partial information is modeled as a decision-dependent distribution, the so-called belief of the leade...

Understanding the strategic behavior of miners in a blockchain is of great importance for its proper operation. A common model for mining games considers an infinite time horizon, with players optimizing asymptotic average objectives. Implicitly, this assumes that the asymptotic behaviors are realized at human-scale times, otherwise invalidating cu...

In past decades, the deployment of renewable-energy-based power generators, namely solar photovoltaic (PV) power generators, has been projected to cause a number of new difficulties in planning, monitoring, and control of power distribution grids. In this paper, a control scheme for flexible asset management is proposed with the aim of closing the...

The present paper is a continuation of a previous work with conditions for regularity of the metric projection. Here we provide a full quantitative characterization of closed bodies in Hilbert spaces with Cp+1-smooth boundary in terms of the smoothness of the metric projection and the behavior of its first derivative.

We show, in Hilbert space setting, that any two convex proper lower semicontinuous functions bounded from below, for which the norm of their minimal subgradients coincide, they coincide up to a constant. Moreover, under classic boundary conditions, we provide the same results when the functions are continuous and defined over an open convex domain....

Motivated by the design and optimization of the water exchange networks in Eco-Industrial Parks (EIP), we investigate the abstract Blind-Input model for general exchange networks. This abstract model is based on a Game Theory approach, formulating it as a Single-Leader-Multi-Follower (SLMF) game: at the upper level, there is an authority (leader) t...

in recent years, growing penetration of renewable-energy-based distributed generation into power distribution grids has been compromising operational constraints. In this paper, a model-based predictive control (MPC) strategy is proposed for demand/supply balance and voltage regulation in a power distribution grid with prolific distributed generati...

in recent years, growing penetration of renewable-energy-based distributed generation into power distribution grids has been compromising operational constraints. In this paper, a model-based predictive control (MPC) strategy is proposed for demand/supply balance and voltage regulation in a power distribution grid with prolific distributed generati...

This paper explores two new paradigms by studying the techno-economic relevance of a concentrated solar power plant in spot electricity markets involving strong price variations, and by investigating the integration of an innovative thermal storage performed by a thermochemical process in such plant. Its aim is to optimize simultaneously the physic...

The property of continuous differentiability with Lipschitz derivative of the square distance function is known to be a characterization of prox-regular sets. We show in this paper that the property of higher-order continuous differentiability with locally uniformly continuous last derivative of the square distance function near a point of a set ch...

Quasi-variational inequalities are variational inequalities in which the constraint map depends on the current point. Due to this characteristic, specific proofs have been built to prove adapted existence results. Semicontinuity and generalized monotonicity are assumed and many efforts have been made in the last decades to use the weakest concepts....

Projected differential equations are known as fundamental mathematical models in economics, for electric circuits, etc. The present paper studies the (higher order) derivability as well as a generalized type of derivability of solutions of such equations when the set involved for projections is prox-regular with smooth boundary. © 2019 American Ins...

Thermal storage is a key point for the development of concentrated solar power technologies. This article aims to develop a methodology for the optimization, from an economic point of view, of a Concentrated Solar Power plant with thermal storage. It addresses two original aspects: (1) it incorporates a thermochemical storage process; (2) it consid...

Based on a fundamental work of R. B. Holmes from 1973, we study differentiability properties of the metric projection onto prox-regular sets. We show that if the set is a nonconvex body with a $C^{p+1}$-smooth boundary, then the projection is $C^{p}$-smooth near suitable open truncated normal rays, which are determined only by the function of prox-...

We introduce the notion of convex smooth-like (resp. w∗-smooth-like) properties, which are a generalization of the well-known Asplund (resp. w∗-Asplund) prop- erty. We show that many of the reductions made for the Asplund property also work for these smooth-like properties. In this framework, we introduce a new geometrical property, called the Face...

This work is divided in two parts: In the first part, we present an integration result in locally convex spaces for a large class of nonconvex functions which enables us to recover the closed convex envelope of a function from its convex subdifferential. Motivated by this, we introduce the class of Subdifferential Dense Primal Determined (SDPD) spa...

We introduce the notions of extended topological vector spaces and extended seminormed spaces, following the main ideas of extended normed spaces, which were introduced by G. Beer and J. Vanderwerff. We provide a topological study of such structures, giving a unifying theory with main applications in the study of spaces of continuous functions. We...

We extend results of R. Correa, Y. Garcia and A. Hantoute ["Integration formulas via the (Fenchel) subdifferential of nonconvex functions", Nonlinear Analysis 75(3) (2012) 1188-1201)] dealing with the integration of nonconvex epi-pointed functions using the Fenchel subdifferential. In this line, we prove that the classical formula of Rockafellar in...