A new algorithm for functions optimization via sign decomposition

The optimization of multivariable polynomic functions depending on bounded parameters of a vector element of an uncertainty parametric box is considered in this paper. A new algorithm is proposed, its basis relies on Sign Decomposition, a mathematical tool previously developed and published by the author and briefly described in this paper. In the new algorithm are applied a partition box procedure and the upper and lower bounds of the function on each box obtained by means of sign decomposition. All the boxes that don\´t contain the minimum of the function are eliminated of the boxes set. The "upper" and "lower" boxes of the new boxes set are substituted by their corresponding partitioned boxes set. The new boxes set is analyzed again and the procedure is applied iteratively until the difference between the upper and lower bounds of the function on the boxes set satisfy a preestablished tolerance. Finally the global minimum value of the function and its coordinates are obtained. The new proposed algorithm doesn\´t use: approximation of functions, derivatives, heuristic, random, initial coordinate or values for start, probabilistic, neural networks, fuzzy logic, learning system or fractal curves methods. The application of the proposed algorithm is very fast and can be used in nonconvex functions in the analysis and design in many disciplines including parametric robust control.