RT journal article
T1 Minimization over Nonconvex Sets
A1 Vílchez Membrilla, José Antonio
A1 Salas Moreno, Víctor
A1 Moreno Pulido, Soledad
A1 Sánchez Alzola, Alberto
A1 Cobos Sánchez, Clemente
A1 García Pacheco, Francisco Javier
A2 Estadística e Investigación Operativa
A2 Ingeniería en AutomáticaElectrónica, Arquitectura y Redes de Computadores
A2 Matemáticas
K1 multioptimization
K1 pareto optimality
K1 normed spaces
K1 matrix norms
K1 ordered lattices
AB Minimum norm problems consist of finding the distance of a closed subset of a normed space to the origin. Usually, the given closed subset is also asked to be convex, thus resulting in a convex minimum norm problem. There are plenty of techniques and algorithms to compute the distance of a closed convex set to the origin, which mostly exist in the Hilbert space setting. In this manuscript, we consider nonconvex minimum norm problems that arise from Bioengineering and reformulate them in such a way that the solution to their reformulation is already known. In particular, we tackle the problem of (Formula presented.) subject to (Formula presented.) for (Formula presented.), where (Formula presented.) and (Formula presented.) are continuous linear operators between real normed spaces (Formula presented.), and (Formula presented.) for (Formula presented.). Notice that the region of constraints of the previous problem is neither convex nor balanced. However, it is additively symmetric, which is also the case for the objective function, due to the properties satisfied by norms, which makes possible the analytic resolution of such a nonconvex minimization. The recent literature shows that the design of optimal coils for electronics applications can be achieved by solving problems like this. However, in this work, we apply our analytical solutions to design an optimal coil for an electromagnetic sensor.
PB MDPI
SN 2073-8994
YR 2024
FD 2024
LK http://hdl.handle.net/10498/35705
UL http://hdl.handle.net/10498/35705
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 22-sep-2026