A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
A randomized algorithm to optimize over certain convex sets
Mathematics of Operations Research
A new algorithm for minimizing convex functions over convex sets
Mathematical Programming: Series A and B
Random walks and an O*(n5) volume algorithm for convex bodies
Random Structures & Algorithms
A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Introduction to Linear Optimization
Introduction to Linear Optimization
Efficient algorithms for universal portfolios
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
An energy-driven approach to linkage unfolding
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
A simple polynomial-time rescaling algorithm for solving linear programs
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Active learning of label ranking functions
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Online convex optimization in the bandit setting: gradient descent without a gradient
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On exact learning halfspaces with random consistent hypothesis oracle
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
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In breakthrough developments about two decades ago, L. G. Khachiyan [14] showed that the Ellipsoid method solves linear programs in polynomial time, while M. Grötschel, L. Lovász and A. Schrijver [4, 5] extended this to the problem of minimizing a convex function over any convex set specified by a separation oracle. In 1996, P. M. Vaidya [21] improved the running time via a more sophisticated algorithm. We present a simple new algorithm for convex optimization based on sampling by a random walk; it also solves for a natural generalization of the problem.