E-Learning Guelma

Optimization is central to any problem involving decision making, whether in engineering or in economics. The task of decision making entails choosing between various alternatives. This choice is governed by our desire to make the "best" decision. The measure of
goodness of the alternatives is described by an objective function or performance index.
Optimization theory and methods deal with selecting the best alternative in the sense of
the given objective function.
The area of optimization has received enormous attention in recent years, primarily because of the rapid progress in computer technology, including the development and availability of user-friendly software, high-speed and parallel processors, and artificial neural
networks. A clear example of this phenomenon is the wide accessibility of optimization
software tools such as the Optimization Toolbox of MATLAB1 and the many other commercial software packages. There are currently several excellent graduate textbooks on
optimization theory and methods (e.g., [1], [5], [6], [8], [9], [10], [12], [15]), as well as undergraduate textbooks on the subject with an emphasis on engineering design (e.g., [1]).
However, there is a need for an introductory textbook on optimization theory and methods
at a senior undergraduate or beginning graduate level. The present text was written with
this goal in mind. The material is an outgrowth of our lecture notes for a one-semester
course in optimization methods for seniors and beginning

This course focuses on Hilbert analysis. Hilbert analysis is a fundamental tool in mathematics and physics in general, and in quantum mechanics in particular.

This course is divided into two main parts:

The first part deals with the structure of a Hilbert space as a vector space on which an inner product is defined. This inner product generates a norm, and this space equipped with this norm is a complete space. We study all the important properties of this space, such as the Cauchy-Schwarz inequality, Bessel's inequality, Fourier series, etc.

The second part is devoted to bounded linear operators defined on this type of spaces.

Crédits : 5            Coefficient : 3

 Faire découvrir à l’étudiant une nouvelle théorie qui est la théorie de la mesure ainsi que son application aux probabilités, le plaçant dans un nouveau contexte d’espaces qui sont les espaces mesurés, par suite une large théorie sur l’intégration est définie, en particulier celle de Lebesgue lui permettant de se familiariser avec les grands résultats de l’intégration tels le théorème de la convergence dominée de Lebesgue et les théorèmes de Fubini.