... if a=b(mod m) and 0≤b≤m−1; hence, a mod m is the smallest nonnegative residue of a modulo m. We have obviously for: Equation 23 And for: Equation 24 We use the transformations: Equation 25   Equation 26 for global optimization...

... applications is related to global optimization. Multivariable optimization problems coming from operational research or from industry can be quickly and easily solved. Originality/value The paper presents a new method based on α‐dense curves for solving Diophantine equations. Consider...

...‐densification technique and adding the new concept of sequence of α‐dense curves with accumulated density to improve the resolution of some global optimization problems. Findings It is found that the new technique based on sequences of α‐dense curves with accumulated densities allows...

... Cybernetics Global optimization The Alienor method, proposed by Yves Cherruault in the early 1980s (see, for instance, Ammar and Cherruault (1993) and Cherruault (1990)), was invented as a minimization technique of the functional error, i.e. the function depending on the solutions of the mathematical...

... be used to improve the stability of insulin formulations. We believe that, with small modifications to the model, the method and algorithms presented in this article can be applied to other protein‐ligand systems. © MCB UP Limited 2000 Cybernetics Global optimization Modelling Algorithms...

...A. Ziadi; Y. Cherruault; G. Mora Some results concerning the existence of α‐dense curves with minimal length are given. This type of curves used in the reducing transformation called Alienor was invented by Cherruault and Guillez. They have been applied to global optimization in the following way...

...A. Ziadi; Y. Cherruault The reducing transformation and global optimization technique called Alienor has been developed in the 1980s by Cherruault and Guillez. These methods are based on the approximating properties of α ‐dense curves. The aim of this work is to give a very large class of functions...

..., the same problem has no solution if we consider the family of curves defined by means of the graphics of continuous and rectifiable functions f: J→ J. Their consequences on the approximation method to the global optimization are also derived. We have just seen that the densification problem...

... as in the above representations, in Ammar and Cherruault (1993) and Cherruault (1990) we can see a deterministic method (called ALIENOR) for the global optimization of a given continuous function f defined on a compact set H of Rⁿ. This method consists of the global optimization of the restriction of f...

...Yves Cherruault We describe two new methods: the global optimization method ALIENOR and the decompositional method of Adomian. Then we show how they can be applied to models identification and to optimal control of biological processes. This paper is dedicated to Professor Jacques‐Louis...