arXiv subjects

Víctor Casero-Alonso

Publications and source records attributed to Víctor Casero-Alonso.

3 recordsLinked to original sources

arXiv2025

A Study on the Optimal Design of Isothermal Experiments in Predictive Microbiology

This study addresses from the Optimal Experimental Design perspective the use of the isothermal experimentation procedure to precisely estimate the parameters defining models used in predictive microbiology. Starting from a case study set out in the literature, and taking the Baranyi model as the primary model, and the Ratkowsky square-root model as the secondary, D- and c-optimal designs are provided for isothermal experiments, taking the temperature both as a value fixed by the experimenter and as a variable to be designed. The designs calculated show that those commonly used in practice are not efficient enough to estimate the parameters of the secondary model, leading to greater uncertainty in the predictions made via these models. Finally, an analysis is carried out to determine the effect on the efficiency of the possible reduction in the final experimental time.

stat.AP↗

arXiv2019

On the convergence of cutting-plane methods for robust optimization with ellipsoidal uncertainty sets

Recent advances in cutting-plane strategies applied to robust optimization problems show that they are competitive with respect to problem reformulations and interior-point algorithms. However, although its application with polyhedral uncertainty sets guarantees convergence, finite termination when using ellipsoidal uncertainty sets is not theoretically guaranteed. This paper demonstrates that the cutting-plane algorithm set out for ellipsoidal uncertainty sets in its more general form also converges in a finite number of steps.

math.OC↗

arXiv2017

Robust solutions of uncertain mixed-integer linear programs using decomposition techniques

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii) binary decisions and iii) hard constraints within an ellipsoidal uncertainty set, this paper provides a different interpretation of their robust counterpart (RC) inspired from decomposition techniques. This new interpretation allows the proposal of an ad-hoc decomposition technique to solve the RC problem with the following advantages: i) it improves tractability, specially for large-scale problems, and ii) it provides the exact probability of constraint violation in case the probability distribution of uncertain parameters are completely defined by using first and second-order probability moments. An attractive aspect of our method is that it decomposes the second-order cone programming problem, associated with the robust counterpart, into a linear master problem and different quadratically constrained problems (QCP) of considerable lower size. The optimal solution is achieved through the solution of these master and subproblems within an iterative scheme based on cutting plane approximations of the second-order cone constraints. In addition, proof of convergence of the iterative method is given.

math.NA↗