| dc.contributor | Velasco Gregory, Mauricio Fernando | |
| dc.contributor | Junca Peláez, Mauricio José | |
| dc.creator | Gálvez Zuleta, Federico | |
| dc.date.accessioned | 2023-08-08T15:35:10Z | |
| dc.date.accessioned | 2023-09-07T00:13:32Z | |
| dc.date.available | 2023-08-08T15:35:10Z | |
| dc.date.available | 2023-09-07T00:13:32Z | |
| dc.date.created | 2023-08-08T15:35:10Z | |
| dc.date.issued | 2023-08-04 | |
| dc.identifier | http://hdl.handle.net/1992/69381 | |
| dc.identifier | instname:Universidad de los Andes | |
| dc.identifier | reponame:Repositorio Institucional Séneca | |
| dc.identifier | repourl:https://repositorio.uniandes.edu.co/ | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/8727204 | |
| dc.description.abstract | En este trabajo se estudia el paper "Low-rank univariate sum of squares has no spurious local minima" de Pablo Parrillo, et al. En el que se trata el problema de estableces si un polinomio univariado es suma de cuadrados mediante la minimización de un objetivo cuadrático que surge de la sustitución de Burer-Monteiro para el problema de programación semidefinida que determina si un polinomio es suma de cuadrados. Este documento estudia el resultado prinicipal del paper que consiste en que todos los mínimos locales de la función objetivo son mínimos globales. | |
| dc.language | spa | |
| dc.publisher | Universidad de los Andes | |
| dc.publisher | Matemáticas | |
| dc.publisher | Facultad de Ciencias | |
| dc.publisher | Departamento de Matemáticas | |
| dc.relation | G. Blekherman. Nonnegative polynomials and sums of squares. J. Amer. Math. Soc., 25(3):617-635, 2012. | |
| dc.relation | G. Blekherman. Nonnegative polynomials and sums of squares. In Semidefinite optimization
and convex algebraic geometry, volume 13 of MOS-SIAM Ser. Optim., pages 159-202. SIAM,
Philadelphia, PA, 2013. | |
| dc.relation | G. Blekherman, P. A. Parrilo, and R. R. Thomas. Semidefinite Optimization and Convex
Algebraic Geometry. Society for Industrial and Applied Mathematics, USA, 2012. | |
| dc.relation | S. Boyd and L. Vandenberghe. Convex optimization. Cambridge University Press, Cambridge,
2004. | |
| dc.relation | S. Burer and R. D. C. Monteiro. A nonlinear programming algorithm for solving semidefi-
nite programs via low-rank factorization. volume 95, pages 329-357. 2003. Computational
semidefinite and second order cone programming: the state of the art. | |
| dc.relation | D. Cifuentes. On the Burer-Monteiro method for general semidefinite programs. Optim. Lett.,
15(6):2299-2309, 2021. | |
| dc.relation | B. Legat, C. Yuan, and P. A. Parrilo. Low-rank univariate sum of squares has no spurious local
minima. https://arxiv.org/abs/2205.11466, 2022. | |
| dc.relation | A. Prestel and C. N. Delzell. Positive polynomials. Springer Monographs in Mathematics.
Springer-Verlag, Berlin, 2001. From Hilbert's 17th problem to real algebra. | |
| dc.rights | https://repositorio.uniandes.edu.co/static/pdf/aceptacion_uso_es.pdf | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.rights | http://purl.org/coar/access_right/c_abf2 | |
| dc.title | Inexistencia de falsos mínimos locales para Burer-Monteiro de rango 2 que codifica la descomposición en suma de cuadrados | |
| dc.type | Trabajo de grado - Pregrado | |
