Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 72, 2023 - Issue 2
176
Views
1
CrossRef citations to date
0
Altmetric
Articles

Critical point theory for sparse recovery

ORCID Icon &
Pages 521-549 | Received 11 Aug 2020, Accepted 09 Sep 2021, Published online: 26 Sep 2021

References

  • Davenport MA, Duarte MF, Eldar YC, et al. Introduction to compressed sensing. In Eldar YC, Kutyniok G, editors. Compressed sensing: theory and applications. Cambridge: Cambridge University Press; 2012. p. 1–64.
  • Beck A, Eldar YC. Sparsity constrained nonlinear optimization: optimality conditions and algorithms. SIAM J Optim. 2013;24:1480–1509.
  • Beck A, Hallak N. On the minimization over sparse symmetric sets: projections, optimality conditions, and algorithms. Math Oper Res. 2016;41:196–223.
  • Beck A, Hallak N. Proximal mapping for symmetric penalty and sparsity. SIAM J Optim. 2018;28:496–527.
  • Burdakov OP, Kanzow C, Schwartz A. Mathematical programs with cardinality constraints: reformulation by complementarity-type conditions and a regularization method. SIAM J Optim. 2016;26:397–425.
  • Červinka M, Kanzow C, Schwartz A. Constraint qualifications and optimality conditions for optimization problems with cardinality constraints. Math Program. 2016;160:353–377.
  • Bucher M, Schwartz A. Second-order optimality conditions and improved convergence results for regularization methods for cardinality-constrained optimization problems. J Optim Theory Appl. 2018;178:383–410.
  • Jongen H Th, Shikhman V, Rückmann J-J. MPCC: critical point theory. SIAM J Optim. 2009;20:473–484.
  • Jongen H Th, Shikhman V. General semi-infinite programming: critical point theory. Optim. 2011;60:859–873.
  • Dorsch D, Shikhman V, Stein O. Mathematical programs with vanishing constraints: critical point theory. J Global Optim. 2012;52:591–605.
  • Kojima M. Strongly stable stationary solutions in nonlinear programs. In S. M. Robinson, editor. Analysis and computation of fixed points. New York (NY): Academic Press; 1980. p. 93–138.
  • Lämmel S, Shikhman V. On nondegenerate M-stationary points for sparsity constrained nonlinear optimization. J Global Optim. 2021. https://doi.org/10.1007/s10898-021-01070-7.
  • Lancaster P. Theory of matrices. London: Academic Press; 1969.
  • Th. Jongen H, Jonker P, Twilt F. Nonlinear optimization in finite dimensions. Dordrecht: Kluwer Academic Publishers; 2000.
  • Th. Jongen H, Shikhman V, Steffensen S. Characterization of strong stability for C-stationary points in MPCC. Math Program. 2012;132:295–308.
  • Goresky M, MacPherson R. Stratified morse theory. New York (NY): Springer; 1988.
  • Goerss PG, Jardine JF. Simplicial homotopy theory. Basel: Birkhäuser; 2009.
  • Spanier EH. Algebraic topology. New York (NY): McGraw-Hill Book Company; 1966.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.