A differential-equations algorithm for nonlinear equations
ACM Transactions on Mathematical Software (TOMS)
Algorithm 617: DAFNE: a differential-equations algorithm for nonlinear equations
ACM Transactions on Mathematical Software (TOMS)
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Algorithm 667: Sigma—a stochastic-integration global minimization algorithm
ACM Transactions on Mathematical Software (TOMS)
A Non-myopic Utility Function for Statistical Global Optimization Algorithms
Journal of Global Optimization
A Stochastic Algorithm for Constrained Global Optimization
Journal of Global Optimization
Convergence analysis of a global optimization algorithm using stochastic differential equations
Journal of Global Optimization
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Parallelizing a global optimization method in a distributed-memory environment
EURO-PDP'00 Proceedings of the 8th Euromicro conference on Parallel and distributed processing
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SIGMA is a set of FORTRAN subprograms for solving the global optimization problem, which implements a method founded on the numerical solution of a Cauchy problem for a stochastic differential equation inspired by statistical mechanics.This paper gives a detailed description of the method as implemented in SIGMA and reports the results obtained by SIGMA attacking, on two different computers, a set of 37 test problems which were proposed elsewhere by the present authors to test global optimization software.The main conclusion is that SIGMA performs very well, solving 35 of the problems, including some very hard ones.Unfortunately, the limited results available to us at present do not appear sufficient to enable a conclusive comparison with other global optimization methods.