Exact Solutions to the Maxmin Problem max‖Ax‖ Subject to ‖Bx‖≤1

• Published in: Mathematics (Basel) Vol. 8; no. 1; p. 85
• Main Authors: Moreno-Pulido, Soledad, Garcia-Pacheco, Francisco Javier, Cobos-Sanchez, Clemente, Sanchez-Alzola, Alberto
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.01.2020; MDPI
• Subjects: Banach spaces; Coils; Exact solutions; Food science; Mathematical analysis; Mathematical functions; Mathematics; matrix norm; maxmin; optimal geolocation; Optimization; Principal components analysis; supporting vector; tms coil; Vectors (mathematics); maxmin; TMS coil; 49J30; 47L90; optimal geolocation MSC: 47L05; maxmin supporting vector matrix norm TMS coil optimal geolocation MSC: 47L05; 90B50; supporting vector; matrix norm

In this manuscript we provide an exact solution to the maxmin problem max ∥ A x ∥ subject to ∥ B x ∥ ≤ 1 , where A and B are real matrices. This problem comes from a remodeling of max ∥ A x ∥ subject to min ∥ B x ∥ , because the latter problem has no solution. Our mathematical method comes from the...