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The Use of Certain Equations of Mathematical Physics in Optimization of a Function on a Set. II

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Abstract

The use of Helmholtz (diffraction and diffusion) and heat conductivity equations for global optimization is described in Part I. Here numerical realization of these ideas is studied and the superlinear rate of convergence is demonstrated. Numerical methods are based on the idea that the solutions of diffraction (diffusion) equations ϕ(x,ω) and heat conductivity equation U(x,t) are convex and concave functions, respectively, in the neighborhood of the point of global minimum in some modified aim function for which the point of global minimum does not change. An idea for the construction of iterative algorithms is developed, in which a programmer, using computation results, actively participates in computations, instructing the computer as to which domains and distribution densities of random vectors are to be used.

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  1. Smolenskenergo, Inc., Smolensk, Russia

    I. M. Prudnikov

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  1. I. M. Prudnikov
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Prudnikov, I.M. The Use of Certain Equations of Mathematical Physics in Optimization of a Function on a Set. II. Automation and Remote Control 63, 1891–1899 (2002). https://doi.org/10.1023/A:1021631112889

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