https://orcid.org/0000-0002-4158-0828
References
- Polyak BT. Convexity of quadratic transformations and its use in control and optimization. J Optim Theory Appl. 1998;99:553–583.
- Dines LL. On the mapping of quadratic forms. Bull Am Math Soc. 1941;47:494–498.
- Baccari A, Samet B. An extension of Polyak's theorem in a Hilbert space. J Optim Theory Appl. 2009;140:409–418.
- Brickman L. On the field of values of a matrix. Proc Am Math Soc. 1961;12:61–66.
- McIntosh A. The Toeplitz–Hausdorff theorem and ellipticity conditions. Am Math Monthly. 1978;85:475–477.
- Martínez-Legaz JE. On Brickman's theorem. J Convex Anal. 2005;12:139–143.
- Micchelli CA. Optimal estimation of linear operators from inaccurate data: a second look. Numer Algorithms. 1993;5:375–390.
- Hestenes MR. Pairs of quadratic forms. Linear Algebra Appl. 1968;1:397–407.
- de Barra G, Giles JR, Sims B. On the numerical range of compact operators on Hilbert spaces. J London Math Soc. 1972;2:704–706.
- Halmos PR. Hilbert space problem book. 2nd ed., New York: Springer-Verlag; 1982.
- Calabi E. Linear systems of real quadratic forms. Proc Am Math Soc. 1964;15:844–846.
- Flores-Bazán F, Opazo F. Characterizing the convexity of joint-range for a pair of inhomogeneous quadratic functions and strong duality. Minimax Theory Appl. 2016;1:257–290.
- Douglas RG. On majorization, factorization and range inclusion of operators in Hilbert space. Proc Am Math Soc. 1966;17:413–415.
- Anderson WN, Trapp GE. Shorted operators II. SIAM J Appl Math. 1975;28:60–71.
- Contino M, Fongi G, Maestripieri A, et al. Total least squares problems on infinite dimensional spaces. Inverse Probl. 2021;37:045008.
- Pólik I, Terlaky T. A survey of the S-lemma. SIAM Rev. 2007;49:371–418.
- Beck A, Ben-Tal A. On the solution of the Tikhonov regularization of the total least squares problem. SIAM J Optim. 2006;17:98–118.
- Golub GH, Hansen PC, O'Leary DP. Tikhonov regularization and total least squares. SIAM J Matrix Anal Appl. 1999;21:185–194.
- de Klerk E, Roos C, Terlaky T. Nonlinear optimization, Lecture notes. Delft, The Netherlands: University of Technology; 2003. p. 1–65.
- Stoer J, Witzgall C. Convexity and optimization in finite dimensions I. Vol. 163, Berlin: Springer Science & Business Media; 2012.
- Nguyen HQ, Chu YC, Sheu RL. On the convexity for the range set of two quadratic functions. J Ind Manag Optim. 2022;18:575–592.