Free Access
Volume 25, 2019
Article Number 56
Number of page(s) 27
Published online 25 October 2019
  1. K.M. Anstreicher, Linear programming in Formula operations. SIAM J. Optim. 9 (1999) 803–812 [Google Scholar]
  2. D.P. Bertsekas, Nonlinear Programming. 2nd edn. Athena Scientific, Belmont, MA (1999) [Google Scholar]
  3. D.P. Bertsekas, Convex Optimization Theory. Athena Scientific, Belmont, MA (2009) [Google Scholar]
  4. E. J. Candes and Y. Plan, A probabilistic and RIPless theory of compressed sensing. IEEE Trans. Inf. Theory 57 (2011) 7235–7254 [Google Scholar]
  5. E. Candes and T. Tao, The Dantzig selector: statistical estimation when p is much larger than n. Ann. Stat. 35 (2007) 2313–2351 [Google Scholar]
  6. F. Facchinei and J.-S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems. Spring-Verlag, New York (2003) [Google Scholar]
  7. S. Foucart and D. Koslicki, Sparse recovery by means of nonnegative least squares. IEEE Signal Process. Lett. 21 (2014) 498–502 [Google Scholar]
  8. S. Foucart and H. Rauhut, A Mathematical Introduction to Compressive Sensing. Birkhäuser, Basel, Switzerland (2013) [CrossRef] [Google Scholar]
  9. J.J. Fuchs, On sparse representations in arbitrary redundant bases. IEEE Trans. Inf. Theory 50 (2004) 1341–1344 [Google Scholar]
  10. J.C. Gilbert, On the solution uniqueness characterization in the L1 norm and polyhedral gauge recovery. J. Optim. Theory Appl. 172 (2017) 70–101 [Google Scholar]
  11. Y. Itoh, M.F. Duarte and M. Parente. Perfect recovery conditions for non-negative sparse modeling. IEEE Trans. Signal Process. 65 (2017) 69–80 [Google Scholar]
  12. S.J. Kim, K. Koh, S. Boyd and D. Gorinevsky, 1 trend filtering. SIAM Rev. 51 (2009) 339–360 [CrossRef] [Google Scholar]
  13. O.L. Mangasarian, Uniqueness of solution in linear programming. Linear Algebra Appl. 25 (1979) 151–162 [Google Scholar]
  14. A. Rinaldo, Properties and refinements of the fused lasso. Ann. Stat. 37 (2009) 2922–2952 [Google Scholar]
  15. R.T. Rockafellar, Convex Analysis. Princeton University Press (1970) [CrossRef] [Google Scholar]
  16. A.P. Ruszczynski, Nonlinear Optimization. Princeton University Press (2006) [CrossRef] [Google Scholar]
  17. S. Scholtes, Introduction to Piecewise Differentiable Equations. Habilitation thesis, Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe (1994) [Google Scholar]
  18. J. Shen, Robust non-Zenoness of piecewise affine systems with applications to linear complementarity systems. SIAM J. Optim. 24 (2014) 2023–2056 [Google Scholar]
  19. J. Shen and T.M. Lebair, Shape restricted smoothing splines via constrained optimal control and nonsmooth Newton’s methods. Automatica 53 (2015) 216–224 [CrossRef] [Google Scholar]
  20. J. Shen and S. Mousavi, Least sparsity of p-norm based optimization problems with p > 1. SIAM J. Optim. 28 (2018) 2721–2751 [Google Scholar]
  21. J. Shen and X. Wang, Estimation of monotone functions via P-splines: a constrained dynamical optimization approach. SIAM J. Control Optim. 49 (2011) 646–671 [CrossRef] [Google Scholar]
  22. J. Shen, L. Han and J.-S. Pang, Switching and stability properties of conewise linear systems. ESAIM: COCV 16 (2010) 764–793 [CrossRef] [EDP Sciences] [Google Scholar]
  23. R.J. Tibshirani, The Lasso problem and uniqueness. Electron. J. Stat. 7 (2013) 1456–1490 [Google Scholar]
  24. R. J. Tibshirani, The Solution Path of the Generalized LASSO. Ph.D. thesis, Stanford University (2011) [Google Scholar]
  25. R. Tibshirani and J. Taylor, Degrees of freedom in Lasso problems. Ann. Stat. 40 (2012) 1198–1232 [Google Scholar]
  26. R. Tibshirani, M. Saunders, S. Rosset, J. Zhu and K. Knight, Sparsity and smoothness via the fused Lasso. J. R. Stat. Soc.: B (Statistical Methodology) 67 (2005) 91–108 [CrossRef] [MathSciNet] [Google Scholar]
  27. M. Wang, W. Xu and A. Tang, A unique “nonnegative” solution to an underdetermined system: from vectors to matrices. IEEE Trans. Signal Process. 59 (2011) 1007–1016 [Google Scholar]
  28. H. Zhang, W. Yin and L. Cheng, Necessary and sufficient conditions of solution uniqueness in 1-norm minimization. J. Optim. Theory Appl. 164 (2015) 109–122 [Google Scholar]
  29. H. Zhang, M. Yan and W. Yin, One condition for solution uniqueness and robustness of both 1-synthesis and 1-analysis minimizations. Adv. Comput. Math. 42 (2016) 1381–1399 [Google Scholar]
  30. Y.-B. Zhao, RSP-based analysis for sparest and least 1-norm solutions to underdetermined linear systems. IEEE Trans. Signal Process. 61 (2013) 5777–5788 [Google Scholar]
  31. Y.-B. Zhao, Equivalence and strong equivalence between the sparsest and least 1 -norm nonnegative solutions of linear systems and their applications. J. Oper. Res. Soc. China 2 (2014) 171–193 [CrossRef] [Google Scholar]
  32. Y.-B. Zhao, Sparse Optimization Theory and Methods. CRC Press, Taylor & Francis, NY (2018) [CrossRef] [Google Scholar]
  33. Y.-B. Zhao and C. Xu, 1-bit compressive sensing: reformulation and RRSP-based sign recovery theory. Sci. China Math. 59 (2016) 2049–2074 [Google Scholar]

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