Journal ArticleDOI
A global optimization algorithm using stochastic differential equations
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The main conclusion is that SIGMA performs very well, solving 35 of the problems, including some very hard ones, and does not appear sufficient to enable a conclusive comparison with other global optimization methods.Abstract:
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.read more
Citations
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References
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Journal ArticleDOI
Optimization by Simulated Annealing
TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
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Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
TL;DR: In this paper, Schnabel proposed a modular system of algorithms for unconstrained minimization and nonlinear equations, based on Newton's method for solving one equation in one unknown convergence of sequences of real numbers.
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Numerical methods for unconstrained optimization and nonlinear equations
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.
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Theory and Applications of Stochastic Differential Equations
Zeev Schuss,Robert O'Malley +1 more
TL;DR: Presents theory, sources, and applications of stochastic differential equations of Ito's type; those containing white noise; and the role of partial differential equations in this context.
Journal ArticleDOI
The Tunneling Algorithm for the Global Minimization of Functions
A. V. Levy,A. Montalvo +1 more
TL;DR: In this paper, the authors considered the problem of finding the global minima of a function and presented an algorithm composed of a sequence of subsequences of c-minima functions.