arXiv subjects

Juan Parra

Publications and source records attributed to Juan Parra.

6 recordsLinked to original sources

arXiv2025

Lispchitz modulus of the argmin mapping in convex quadratic optimization

This paper was initially motivated by the computation of the Lipschitz modulus of the metric projection on polyhedral convex sets in the Euclidean space when both the reference point and the polyhedron where it is projected are subject to perturbations. The paper tackles the more general problem of computing the Lipschitz modulus of the argmin mapping in the framework of canonically perturbed convex quadratic problems. We point out the fact that a point-based formula (depending only on the nominal data) for such a modulus is provided. In this way, the paper extends to the current quadratic setting some results previously developed in linear programming. As an application, we provide a point-based formula for the Lipschitz modulus of the metric projection on a polyhedral convex set.

math.OC↗

arXiv2025

Lipschitz upper semicontinuity of linear inequality systems under full perturbations

The present paper is focused on the computation of the Lipschitz upper semicontinuity modulus of the feasible set mapping in the context of fully perturbed linear inequality systems; i.e., where all coefficients are allowed to be perturbed. The direct antecedent comes from the framework of right-hand side (RHS, for short) perturbations. The difference between both parametric contexts, full vs RHS perturbations, is emphasized. In particular, the polyhedral structure of the graph of the feasible set mapping in the latter framework enables us to apply classical results as those of Hoffman [A. J. HOFFMAN, J. Res. Natl. Bur. Stand. 49 (1952), pp. 263--265] and Robinson [S. M. ROBINSON, Math. Progr. Study 14 (1981), pp. 206--214]. In contrast, the graph of the feasible set mapping under full perturbations is no longer polyhedral (not even convex). This fact requires ad hoc techniques to analyze the Lipschitz upper semicontinuity property and its corresponding modulus.

math.OC↗

arXiv2023

The afterglow of GW170817 from every angle: Prospects for detecting the afterglows of binary neutron star mergers

To date GW170817, produced by a binary neutron star (BNS) merger, is the only gravitational wave event with an electromagnetic (EM) counterpart. It was associated with a prompt short gamma-ray burst (GRB), an optical kilonova, and the afterglow of a structured, off-axis relativistic jet. We model the prospects for future mergers discovered in gravitational waves to produce detectable afterglows. Using a model fit to GW170817, we assume all BNS mergers produce jets with the same parameters, and model the afterglow luminosity for a full distribution of observer angles, ISM densities, and distances. We find that in the LIGO/Virgo/KAGRA O4 run, 30% - 45% of BNS mergers with a well-localized counterpart will have an afterglow detectable with current instrumentation in the X-ray, radio and optical. Without a previously detected counterpart, 10% - 15% will have an afterglow detectable by wide-area radio and optical surveys, compared to only about 5% - 12% of events expected to have bright (on-axis) gamma-ray emission. Most afterglows that are detected will be from off-axis jets. Further in the future, in the A+ era (O5), 40% - 50% of mergers will have afterglows detectable with next-generation X-ray and radio instruments. Future wide-area radio survey instruments, particularly DSA-2000, could detect 40% of afterglows, even without a kilonova counterpart. Finding and monitoring these afterglows will provide valuable insight into the structure and diversity of relativistic jets, the rate at which mergers produce jets, and constrain the angle of the mergers relative to our line of sight.

astro-ph.HE↗

arXiv2022

From calmness to Hoffman constants for linear semi-infinite inequality systems

In this paper we focus on different -- global, semi-local and local -- versions of Hoffman type inequalities expressed in a variational form. In a first stage our analysis is developed for generic multifunctions between metric spaces and we finally deal with the feasible set mapping associated with linear semi-infinite inequality systems (finitely many variables and possibly infinitely many constraints) parameterized by their right-hand side. The Hoffman modulus is shown to coincide with the supremum of Lipschitz upper semicontinuity and calmness moduli when confined to multifunctions with a convex graph and closed images in a reflexive Banach space, which is the case of our feasible set mapping. Moreover, for this particular multifunction a formula -- only involving the system's left-hand side -- of the global Hoffman constant is derived, providing a generalization to our semi-infinite context of finite counterparts developed in the literature. In the particular case of locally polyhedral systems, the paper also provides a point-based formula for the (semi-local) Hoffman modulus in terms of the calmness moduli at certain feasible points (extreme points when the nominal feasible set contains no lines), yielding a practically tractable expression for finite systems.

math.OC↗

arXiv2019

Subdifferentials and Stability Analysis of Feasible Set and Pareto Front Mappings in Linear Multiobjective Optimization

The paper concerns multiobjective linear optimization problems in R^n that are parameterized with respect to the right-hand side perturbations of inequality constraints. Our focus is on measuring the variation of the feasible set and the Pareto front mappings around a nominal element while paying attention to some specific directions. This idea is formalized by means of the so-called epigraphical multifunction, which is defined by adding a fixed cone to the images of the original mapping. Through the epigraphical feasible and Pareto front mappings we describe the corresponding vector subdifferentials, and employ them to verifying Lipschitzian stability of the perturbed mappings with computing the associated Lipschitz moduli. The particular case of ordinary linear programs is analyzed, where we show that the subdifferentials of both multifunctions are proportional subsets. We also provide a method for computing the optimal value of linear programs without knowing any optimal solution. Some illustrative examples are also given in the paper.

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arXiv2019

Lipschitz modulus of linear and convex systems with the Hausdorff metric

This paper analyzes the Lipschitz behavior of the feasible set in two parametric settings, associated with linear and convex systems in R^n. To start with, we deal with the parameter space of linear (finite/semi-infinite) systems identified with the corresponding sets of coefficient vectors, which are assumed to be closed subsets of R^(n+1). In this framework, where the Hausdorff distance is used to measure the size of perturbations, an explicit formula for computing the Lipschitz modulus of the feasible set mapping is provided. As direct antecedent, we appeal to its counterpart in the parameter space of all linear systems with a fixed index set, T, where the Chebyshev (pseudo) distance was considered to measure the perturbations. Indeed, the stability (and, particularly, Lipschitz properties) of linear systems in the Chebyshev framework has been widely analyzed in the literature. Here, through an appropriate indexation strategy, we take advantage of previous results to derive the new ones in the Hausdorff setting. In a second stage, the possibility of perturbing directly the set of coefficient vectors of a linear system allows us to provide new contributions on the Lipschitz behavior of convex systems via linearization techniques.

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