Approximating parameterized convex optimization problems

ACM Transactions on Algorithms

Volumn 9, Issue 1, 2012, Pages

  Giesen, Joachim ^a   Jaggi, Martin ^b   Laue, Sören ^c  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^b ETH ZURICH   (Switzerland)

^c CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE SOLUTION; CONVEX OPTIMIZATION PROBLEMS; MINIMUM ENCLOSING BALL; MULTIPLE KERNEL LEARNING; OPTIMALITY; OPTIMIZATION PROBLEMS; PARAMETERIZED; REGULARIZATION PATHS;

CONVEX OPTIMIZATION; OPTIMIZATION; SUPPORT VECTOR MACHINES;

PARAMETERIZATION;

EID: 84872453870     PISSN: 15496325     EISSN: 15496333     Source Type: Journal    
DOI: 10.1145/2390176.2390186     Document Type: Article

References (20)

1. AGARWAL, P., HAR-PELED, S., AND VARADARAJAN, K. 2004. Approximating extent measures of points. J. ACM 51, 4, 606-635.
2. AGARWAL, P., HAR-PELED, S., AND YU, H. 2007. Embeddings of surfaces, curves, and moving points in Euclidean space. In Proceedings of the 23rd Annual Symposium on Computational Geometry (SCG'07).
3. BACH, F., LANCKRIET, G., AND JORDAN, M. 2004. Multiple kernel learning, conic duality, and the SMO algorithm. In Proceedings of the 21st International Conference on Machine Learning (ICML'04).
4. BǍDOIU, M. AND CLARKSON, K. L. 2007. Optimal core-sets for balls. Computat. Geome. Theory Appli. 40, 1, 14-22.
5. CLARKSON, K. L. 2010. Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm. ACM Trans. Algor. 6, 4, 1-30.
6. FRIEDMAN, J., HASTIE, T., HÖFLING, H., AND TIBSHIRANI, R. 2007. Pathwise coordinate optimization. Ann. Appl. Stat. 1, 2, 302-332.
7. GÄRTNER, B. AND JAGGI, M. 2009. Coresets for polytope distance. In Proceedings of the 25th Annual Symposium on Computational Geometry (SCG'09).
8. GÄRTNER, B., JAGGI, M., AND MARIA, C. 2010. An exponential lower bound on the complexity of regularization paths. arXiv.org cs.LG.
9. GIESEN, J., JAGGI, M., AND LAUE, S. 2010. Approximating parameterized convex optimization problems. In Proceedings of the 18th Annual European Symposium on Algorithms (ESA'10). 524-535.
10. GIESEN, J., JAGGI, M., AND WELSCH, T. 2009. A combinatorial algorithm to compute regularization paths. arXiv.org cs.LG.
11. GILBERT, E. G. 1966. An iterative procedure for computing the minimum of a quadratic form on a convex set. SIAM J. Control 4, 1, 61-80.
12. HASTIE, T., ROSSET, S., TIBSHIRANI, R., AND ZHU, J. 2004. The entire regularization path for the support vector machine. J. Mach. Learn. Res. 5, 1391-1415.
13. JAGGI, M. 2011. Sparse convex optimization methods for machine learning. Ph.D. thesis, ETH Z̈ urich, (To appear).
14. MARKOWITZ, H. 1952. Portfolio selection. J. Finance 7, 1, 77-91.
15. MATOUŠEK, J. AND GÄRTNER, B. 2007. Understanding and Using Linear Programming. Springer-Verlag, Inc., New York.
16. MITCHELL, B., DEM'YANOV, V., AND MALOZEMOV, V. 1974. Finding the point of a polyhedron closest to the origin. SIAM J. Control.
17. RAKOTOMAMONJY, A., BACH, F. R., CANU, S., AND GRANDVALET, Y. 2008. SimpleMKL. J. Mach. Learn. Res. 9, 2491-2521.
18. ROSSET, S. AND ZHU, J. 2007. Piecewise linear regularized solution paths. Ann. Stat. 35, 3, 1012-1030.
19. TSANG, I. W., KWOK, J. T., AND CHEUNG, P.-M. 2005. Core vector machines: Fast SVM training on very large data sets. J. Mach. Learn. Res. 6, 363-392.
20. WU, Z., ZHANG, A., LI, C., AND SUDJIANTO, A. 2008. Trace solution paths for SVMs via parametric quadratic programming. In Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. DMMT Workshop.