An Efficient Rescaled Perceptron Algorithm for Conic Systems

Mathematics of Operations Research

Volumn 34, Issue 3, 2009, Pages 621-641

  Belloni, Alexandre ^a   Freund, Robert M ^b   Vempala, Santosh ^c  

^a DUKE UNIVERSITY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c Georgia Institute of Technology   (United States)

Author keywords

Conic system; Convex cones; Perception; Separation oracle

Indexed keywords

CONIC SYSTEM; CONVEX CONE; CONVEX CONES; EUCLIDEAN; FEASIBLE REGIONS; FEASIBLE SOLUTION; HALF SPACES; HIGH PROBABILITY; LINEAR INEQUALITY SYSTEMS; LINEAR PROGRAMS; NATURAL CONDITIONS; NEURODYNAMICS; PERCEPTION; PERCEPTRON; PERCEPTRON ALGORITHMS; POLYNOMIAL-TIME; SECOND ORDER CONE; SEMIDEFINITE CONES; WASHINGTON;

CONES; POLYNOMIAL APPROXIMATION; SEPARATION; SYSTEMS ANALYSIS;

ALGORITHMS;

EID: 70349271230     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1090.0388     Document Type: Article

References (23)

1. Belloni, A., R. M. Freund. 2008. On the second-order feasibility cone: Primal-dual representation and efficient projection. SIAM J. Optim. 19(3) 1073-1092.
2. Berman, A. 1973. Cones, Matrices, and Mathematical Programming. Springer-Verlag, New York.
3. Bertsimas, D., S. Vempala. 2004. Solving convex programs by random walks. J. ACM 51(4) 540-556.
4. Blum, A., A. Frieze, R. Kannan, S. Vempala. 1998. A polynomial-time algorithm for learning noisy linear threshold functions. Algorithmica 22(1) 35-52.
5. Dunagan, J., S. Vempala. 2008. A simple polynomial-time rescaling algorithm for solving linear programs. Math. Programming 114(1)101-114.
6. Freund, R. M., J. R. Vera. 1999. Condition-based complexity of convex optimization in conic linear form via the ellipsoid algorithm. SIAM J. Optim. 10(1) 155-176.
7. Freund, R. M., J. R. Vera. 1999. Some characterizations and properties of the "distance to ill-posedness" and the condition measure of a conic linear system. Math. Programming 86(2) 225-260.
8. Fu, M., Z.-Q. Luo, Y. Ye. 1998. Approximation algorithms for quadratic programming. J. Combin. Optim. 2(1) 29-50.
9. Gradshtein, I. S., I. M. Ryzhik. 2007. Table of Integrals, Series, and Product. Academic Press, New York.
10. Grötschel, M., L. Lovász, A. Schrijver. 1994. Geometric Algorithms and Combinatorial Optimization, 2nd ed. Springer-Verlag, Berlin.
11. Karmarkar, N. 1984. A new polynomial-time algorithm for linear programming. Combinatorica 4(4) 373-395.
12. Khachiyan, L. G. 1979. A polynomial algorithm in linear programming. Soviet Math. Dokl. 20(1) 191-194.
13. Motwani, R., P. Raghanav. 1995. Randomized Algorithms. Cambridge University Press, Cambridge, UK.
14. Nesterov, Y., A. Nemirovskii. 1993. Interior-Point Polynomial Algorithms in Convex Programming. SIAM, Philadelphia.
15. Pataki, G. 1992. On the closedness of the linear image of a closed convex cone. Technical Report TR-02-3, Department of Operations Research, University of North Carolina, Chapel Hill.
16. Renegar, J. 1987. On the worst-case arithmetic complexity of approximating zeros of polynomials. J. Complexity 3(2) 90-113.
17. Renegar, J. 1994. Some perturbation theory for linear programming. Math. Programming 65(1) 73-91.
18. Renegar, J. 1995. Linear programming, complexity theory, and elementary functional analysis. Math. Programming 70(3) 279-351.
19. Rockafellar, R. T. 1970. Convex Analysis. Princeton University Press, Princeton, NJ.
20. Rosenblatt, F. 1962. Principles of Neurodynamics. Spartan Books, Washington, DC.
21. Vavasis, S. A., R. Zippel. 1990. Proving polynomial time for sphere-constrained quadratic programming. Technical report, Department of Computer Science, Cornell University, Ithaca, NY.
22. Wolkowicz, H., R. Saigal, L. Vandenberghe. 2000. Handbook of Semidefinite Programming. Kluwer Academic Publishers, Dordrecht, The Netherlands.
23. Ye, Y. 1992. On affine scaling algorithms for nonconvex quadratic programming. Math. Programming 56(3) 285-300.