abstract: in this thesis, we focus to class of convex optimization problem whose objective function is given as a linear function and a convex function of a linear transformation of the decision variables and whose feasible region is a polytope. we show that there exists an optimal solution to this class of problems on a face of the constraint polytope of feasible region. based on this, we dev...

Background and Aims: In the field of orthodontics, gaining comprehensive information around dento-skeletal complex is necessary to choose the best treatment plan for each patient. The aim of this study was to investigate the linear and angular parameters in panoramic radiographs to find a path to correlate transvers to sagittal dimensions. Materials and Methods: Total number of sixty two, ...

abstract this thesis includes five chapter : the first chapter assign to establish fuzzy mathematics requirement and introduction of liner programming in thesis. the second chapter we introduce a multilevel linear programming problems. the third chapter we proposed interactive fuzzy programming which consists of two phases , the study termination conditions of algorithm we show a satisfac...