Explanipedia

Lipschitz Stability in Convex Optimization Open

M. J. Cánovas, J. Parra · 2025

This work is concerned with the quantitative stability of the feasible and optimal solutions of convex semi-infinite optimization problems in different parametric settings. Regarding the constraint system, we deal with convex inequalities …

Lipschitz upper semicontinuity of linear inequality systems under full perturbations Open

Jesús Camacho, M. J. Cánovas, Helmut Gfrerer, J. Parra · 2025

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…

Feasibility problems via paramonotone operators in a convex setting Open

J. Camacho, M. J. Cánovas, Juan Enrique Martínez-Legaz, J. Parra · 2024

This paper is focussed on some properties of paramonotone operators on Banach spaces and their application to certain feasibility problems for convex sets in a Hilbert space and convex systems in the Euclidean space. In particular, it show…

Hoffman constant of the argmin mapping in linear optimization Open

J. Camacho, M. J. Cánovas, Helmut Gfrerer, J. Parra · 2023

The main contribution of this paper consists of providing an explicit formula to compute the Hoffman constant of the argmin mapping in linear optimization. The work is developed in the context of right-hand side perturbations of the constr…

Feasibility problems via paramonotone operators in a convex setting Open

J. Camacho, M. J. Cánovas, Juan Enrique Martínez-Legaz, J. Parra · 2023

This paper is focused on some properties of paramonotone operators on Banach spaces and their application to certain feasibility problems for convex sets in a Hilbert space and convex systems in the Euclidean space. In particular, it shows…

Robust and continuous metric subregularity for linear inequality systems Open

J. Camacho, M. J. Cánovas, Marco A. López, J. Parra · 2022

From Calmness to Hoffman Constants for Linear Semi-infinite Inequality Systems Open

J. Camacho, M. J. Cánovas, J. Parra · 2022

In this paper we focus on different---global, semilocal, 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…

Stability and Sensitivity of Uncertain Linear Programs Open

M. J. Cánovas, J. Parra · 2022

The present paper deals with uncertain linear optimization problems where the objective function coefficient vector belongs to a compact convex uncertainty set and the feasible set is described by a linear semi-infinite inequality system (…

Lipschitz upper semicontinuity in linear optimization via local directional convexity Open

J. Camacho, M. J. Cánovas, J. Parra · 2022

This work is focussed on computing the Lipschitz upper semicontinuity modulus of the argmin mapping for canonically perturbed linear programs. The immediate antecedent can be traced out from Camacho J et al. [2022. From calmness to Hoffman…

Correction to: Lipschitz modulus of linear and convex inequality systems with the Hausdorff metric Open

Gerald Beer, M. J. Cánovas, Marco A. López, J. Parra · 2021

Projection-Based Local and Global Lipschitz Moduli of the Optimal Value in Linear Programming Open

M. J. Cánovas, M. J. Gisbert, Diethard Klatte, J. Parra · 2021

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

Jesús Camacho, M. J. Cánovas, J. Parra · 2021

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 w…

From calmness to Hoffman constants for linear inequality systems Open

J. Camacho, M. J. Cánovas, J. Parra · 2021

In this paper we deal with (finite) linear inequality systems parameterized by their right-hand side. We show that the sharp Hoffman constant at a given nominal parameter may be expressed as the maximum of the calmness moduli of the feasib…

Calmness of Linear Constraint Systems under Structured Perturbations with an Application to the Path-Following Scheme Open

Carlos Argáez, M. J. Cánovas, J. Parra · 2021

We are concerned with finite linear constraint systems in a parametric framework where the right-hand side is an affine function of the perturbation parameter. Such structured perturbations provide a unified framework for different paramet…

Lipschitz modulus of linear and convex inequality systems with the Hausdorff metric Open

Gerald Beer, M. J. Cánovas, Marco A. López, J. Parra · 2020

This paper analyzes the Lipschitz behavior of the feasible set mapping associated with linear and convex inequality systems in $${\mathbb {R}}^{n}$$ . To start with, we deal with the parameter space of linear (finite/semi-infinite) sy…

Lipschitz lower semicontinuity moduli for linear inequality systems Open

M. J. Cánovas, M. J. Gisbert, R. Henrion, J. Parra · 2020

Preface to the Special Issue Dedicated to Marco A. López’s 70th Birthday Open

M. J. Cánovas, Alexander Y. Kruger, Hoàng Xuân Phú, Michel Théra · 2020

Marco A. López, a Pioneer of Continuous Optimization in Spain Open

M. J. Cánovas, Alexander Y. Kruger, Hoàng Xuân Phú, Michel Théra · 2020

Preface of the Special Issue Error Bounds, Regularity, and Nonsmooth Optimization Open

Regina S. Burachik, M. J. Cánovas, Vera Roshchina, Claudia Sagastizábal · 2020

Marco A. López, a Pioneer of Continuous Optimization in Spain Open

M. J. Cánovas, Alexander Y. Kruger, Hoàng Xuân Phú, Michel Théra · 2019

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

M. J. Cánovas, Marco A. López, Boris S. Mordukhovich, J. Parra · 2019

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 P…

Lipschitz modulus of linear and convex systems with the Hausdorff metric Open

Gerald Beer, M. J. Cánovas, Marco A. López, J. Parra · 2019

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 identifie…

Lipschitz Modulus of the Optimal Value in Linear Programming Open

M. J. Gisbert, M. J. Cánovas, J. Parra, F. Javier Toledo · 2018

Calmness of the Optimal Value in Linear Programming Open

M. J. Gisbert, M. J. Cánovas, J. Parra, F. Javier Toledo · 2018

This research has been partially supported by grant MTM2014-59179-C2-2-P from MINECO, Spain, and FEDER "Una manera de hacer Europa," European Union.

Calmness modulus of fully perturbed linear programs Open

M. J. Cánovas, Abderrahim Hantoute, J. Parra, F. Javier Toledo · 2015

This paper provides operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping in linear optimization under uniquene…

Critical objective size and calmness modulus in linear programming Open

M. J. Cánovas, René Henrion, J. Parra, F. Javier Toledo · 2015

This paper introduces the concept of critical objective size associated with a linear program in order to provide operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating …

Outer limit of subdifferentials and calmness moduli in linear and nonlinear programming Open

M. J. Cánovas, René Henrion, Marco A. López, J. Parra · 2015

With a common background and motivation, the main contributions of this paper are developed in two different directions. Firstly, we are concerned with functions which are the maximum of a finite amount of continuously differentiable funct…

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