Numerical analysis: 4th ed
The globally convexized filled functions for global optimization
Applied Mathematics and Computation
Diffusion equation method of global minimization performance for standard test functions
Journal of Optimization Theory and Applications
Recent advances in global optimization
An introduction to infinite-dimensional linear systems theory
An introduction to infinite-dimensional linear systems theory
Global Continuation for Distance Geometry Problems
SIAM Journal on Optimization
Finding Global Minima with a Computable Filled Function
Journal of Global Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
A note on global optimization via the heat diffusion equation
Journal of Global Optimization
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A new smoothing method of global optimization is proposed in the present paper, which prevents shifting of global minima. In this method, smoothed functions are solutions of a heat diffusion equation with external heat source. The source helps to control the diffusion such that a global minimum of the smoothed function is again a global minimum of the cost function. This property, and the existence and uniqueness of the solution are proved using results in theory of viscosity solutions. Moreover, we devise an iterative equation by which smoothed functions can be obtained analytically for a class of cost functions. The effectiveness and potential of our method are then demonstrated with some experimental results.