Cubic regularization of a Newton scheme and its global performance
Author
Abstract
Suggested Citation
Download full text from publisher
References listed on IDEAS
- B. T. Polyak, 1998. "Convexity of Quadratic Transformations and Its Use in Control and Optimization," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 553-583, December.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- NESTEROV, Yu., 2006. "Cubic regularization of Newton’s method for convex problems with constraints," LIDAM Discussion Papers CORE 2006039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- NESTEROV, Yu, 2003. "Modified Gauss-Newton scheme with worst-case guarantees for its global performance," LIDAM Discussion Papers CORE 2003086, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Polyak, B.T., 2007. "Newton's method and its use in optimization," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1086-1096, September.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Fabián Flores-Bazán & William Echegaray & Fernando Flores-Bazán & Eladio Ocaña, 2017. "Primal or dual strong-duality in nonconvex optimization and a class of quasiconvex problems having zero duality gap," Journal of Global Optimization, Springer, vol. 69(4), pages 823-845, December.
- C. Durieu & É. Walter & B. Polyak, 2001. "Multi-Input Multi-Output Ellipsoidal State Bounding," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 273-303, November.
- de Klerk, E., 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere : A Short Survey," Discussion Paper 2006-85, Tilburg University, Center for Economic Research.
- Zhuoyi Xu & Linbin Li & Yong Xia, 2023. "A partial ellipsoidal approximation scheme for nonconvex homogeneous quadratic optimization with quadratic constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 93-109, August.
- J. B. Lasserre & J. B. Hiriart-Urruty, 2002. "Mathematical Properties of Optimization Problems Defined by Positively Homogeneous Functions," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 31-52, January.
- A. Baccari & B. Samet, 2009. "An Extension of Polyak’s Theorem in a Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 409-418, March.
- Shenglong Hu & Guoyin Li & Liqun Qi, 2016. "A Tensor Analogy of Yuan’s Theorem of the Alternative and Polynomial Optimization with Sign structure," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 446-474, February.
- B. S. Mordukhovich & M. E. Sarabi, 2017. "Stability Analysis for Composite Optimization Problems and Parametric Variational Systems," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 554-577, February.
- Etienne Klerk, 2008. "The complexity of optimizing over a simplex, hypercube or sphere: a short survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 111-125, June.
- Huu-Quang Nguyen & Ruey-Lin Sheu, 2019. "Geometric properties for level sets of quadratic functions," Journal of Global Optimization, Springer, vol. 73(2), pages 349-369, February.
- Immanuel Bomze & Markus Gabl, 2021. "Interplay of non-convex quadratically constrained problems with adjustable robust optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 115-151, February.
- H. Tuy & H. Tuan, 2013. "Generalized S-Lemma and strong duality in nonconvex quadratic programming," Journal of Global Optimization, Springer, vol. 56(3), pages 1045-1072, July.
- de Klerk, E., 2008. "The complexity of optimizing over a simplex, hypercube or sphere : A short survey," Other publications TiSEM 485b6860-cf1d-4cad-97b8-2, Tilburg University, School of Economics and Management.
- Mengmeng Song & Yong Xia, 2023. "Calabi-Polyak convexity theorem, Yuan’s lemma and S-lemma: extensions and applications," Journal of Global Optimization, Springer, vol. 85(3), pages 743-756, March.
- Kürşad Derinkuyu & Mustafa Pınar, 2006. "On the S-procedure and Some Variants," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 55-77, August.
- Gabriel Haeser, 2017. "An Extension of Yuan’s Lemma and Its Applications in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 641-649, September.
- Guoyin Li, 2012. "Global Quadratic Minimization over Bivalent Constraints: Necessary and Sufficient Global Optimality Condition," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 710-726, March.
- M. Ruiz Galán, 2017. "A theorem of the alternative with an arbitrary number of inequalities and quadratic programming," Journal of Global Optimization, Springer, vol. 69(2), pages 427-442, October.
- de Klerk, E., 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere : A Short Survey," Other publications TiSEM 88640b6d-5240-472d-8669-4, Tilburg University, School of Economics and Management.
- Sheng-Long Hu & Zheng-Hai Huang, 2012. "Theorems of the Alternative for Inequality Systems of Real Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 1-16, July.
More about this item
Keywords
general nonlinear optimization; unconstrained optimization; Newton method; trust-region methods; global complexity bounds; global rate of convergence;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cor:louvco:2003041. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.html .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.