Théorie de la programmation non linéaire

1Universit´e Joseph Fourier`emeMaster de Math´ematiques Appliqu´ees , 2 ann´eeEFFICIENT METHODS IN OPTIMIZATIONTh´eorie de la programmation non-lin´eaireAnatoli IouditskiLecture NotesOptimization problems arise naturally in many application fields. Whatever people do,at some point they get a craving for organizing things in a best possible way. This intention,converted in a mathematical form, appears to be an optimization problem of certain type(think of, say, Optimal Diet Problem). Unfortunately, the next step, consisting of finding asolution to the mathematical model is less trivial. At the first glance, everything looks verysimple: many commercial optimization packages are easily available and any user can get a“solution” to his model just by clicking on an icon at the desktop of his PC. However, thequestion is, how much he could trust it?One of the goals of this course is to show that, despite to their attraction, the generaloptimization problems very often break the expectations of a naive user. In order to applythese formulationssuccessfully, itisnecessary to beaware ofsome theory, which tellsuswhatwe can and what we cannot do with optimization problems. The elements of this theory canbe found in each lecture of the course.This course itself is based on the lectures given by Arkadi Nemirovski at Technion in late1990’s. On the other hand all the errors and inanities you may find here should be put onthe account of the name at the title page.http:/ ...