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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 65, 2016 - Issue 10
268
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Articles

On certain optimization problems related to matrix norms

Pages 1791-1803 | Received 09 Nov 2015, Accepted 21 Jul 2016, Published online: 07 Aug 2016

References

  • von Neumann J. Some matrix inequalities and metrixation of metric spaces. Tomsk Unio. Rev. 1937. p. 1286–399; in Collected Works, Pergamon, Oxford, 1962, p. 205–219.
  • Mudholkar GS. A class of tests with monotone power functions for two problems in muhivariate statistical analysis. Ann. Math. Statist. 1965;36:1794–1801.
  • Liu G, Lin Z, Yan S, et al. Robust recovery of subspace structures by low-rank representation. IEEE Trans. Pattern Anal. Mach. Intell. (TPAMI). 2013;35:171–184.
  • Householder AS. The theory of matrices in numerical analysis. New York (NY): Blaisdell; 1964.
  • Doan XV, Vavasis S. Finding approximatately rank-one submatrices with the nuclear norm and {\it l}\textsubscript{1}-norm. SIAM J. Optim. 2013;23:2502–2540.
  • Friedlander MP, Macêdo I, Pong TK. Gauge optimization and duality. SIAM J. Optim. 2014;24:1999–2022.
  • Freund RM. Dual gauge programs, with applications to quadratic programming and the minimum-norm problem. Math. Program. 1987;38:47–67.
  • Fan Ky. Maximum properties and inequalities for the eigenvalues of completely continuous operators. Proc. Nat. Acad. Sci. USA. 1951;37:760–766.
  • Zietak K. On the characterization of the extremal points of the unit sphere of matrices. Linear Algebra Appl. 1988;106:57–75.
  • Stewart G, Sun J. Matrix perturbation theory. Boston (MA): Academic Press; 1990.
  • Rockafellar RT. Convex analysis. Princeton (NJ): Princeton University Press; 1970.
  • Golub GH, Van Loan CF. Matrix computations. 3rd ed. Baltimore: Johns Hopkins University Press; 1996.

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