To study constrained or unconstrained global optimization problems in a cube of Rd where d is a positive integer.
α‐dense curves are initially used to transform this problem into a global optimization problem of a single variable. The optimization of the one variable is then treated by means of the Legendre‐Fenchel Transform. This discrete convex envelope of the one variable function obtained previously, can then be computed.
Global optimization problems of this nature have already been extensively studied by the authors. In this paper they have coupled the Alienor method with Legendre‐Fenchel Tranform to compute a discrete convex envelope of the function to minimize. A fast algorithm was successfully used to do this.
This approach to global optimization is based on α‐dense curves and numerical tests performed on a Pentium IV (1,700 MHz) computer used with Mathematica 4 software.
Gives the solutions illustrated in the numerous examples provided that show the practicality of the methodology.
A new approach based on extensive research into global optimization via α‐dense curves.
