Cooling schedules for optimal annealing
Mathematics of Operations Research
Sampling and integration of near log-concave functions
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Elements of information theory
Elements of information theory
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
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
Introduction to Stochastic Search and Optimization
Introduction to Stochastic Search and Optimization
Solving convex programs by random walks
Journal of the ACM (JACM)
SIAM Journal on Computing
Simulated annealing in convex bodies and an O*(n4) volume algorithm
Journal of Computer and System Sciences - Special issue on FOCS 2003
Simulated annealing for graph bisection
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Adaptive parameterized improving hit-and-run for global optimization
Optimization Methods & Software - GLOBAL OPTIMIZATION
Sampling s-Concave Functions: The Limit of Convexity Based Isoperimetry
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Probabilistic structured predictors
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
A random-sampling-based algorithm for learning intersections of halfspaces
Journal of the ACM (JACM)
Multibandwidth kernel-based object tracking
Advances in Artificial Intelligence - Special issue on machine learning paradigms for modeling spatial and temporal information in multimedia data mining
Survey paper: Research on probabilistic methods for control system design
Automatica (Journal of IFAC)
Pattern discrete and mixed Hit-and-Run for global optimization
Journal of Global Optimization
Distribution free evolvability of polynomial functions over all convex loss functions
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Submodular maximization by simulated annealing
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A dynamic programming approach to efficient sampling from Boltzmann distributions
Operations Research Letters
Adaptive search with stochastic acceptance probabilities for global optimization
Operations Research Letters
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We apply the method known as simulated annealing to the following problem in convex optimization: Minimize a linear function over an arbitrary convex set, where the convex set is specified only by a membership oracle. Using distributions from the Boltzmann-Gibbs family leads to an algorithm that needs only O*(√n) phases for instances in Rn. This gives an optimization algorithm that makes O*(n4.5) calls to the membership oracle, in the worst case, compared to the previous best guarantee of O*(n5). The benefits of using annealing here are surprising because such problems have no local minima that are not also global minima. Hence, we conclude that one of the advantages of simulated annealing, in addition to avoiding poor local minima, is that in these problems it converges faster to the minima that it finds. We also give a proof that under certain general conditions, the Boltzmann-Gibbs distributions are optimal for annealing on these convex problems.