Abstract:
The topic begins with several quadratic programming (QP) models
(1. unconstrained model; 2. QP with linear and symmetric bound constraints; 3. QP with linear bound constraints; 4. QP with one quadratic constraint; 5. QP in standard form).
The solving of QP models 2, 3 and 4 is associated with a neural network frame. For QP models 2 and 3 a preconditioning technique is developed. This technique reduces the susceptibility of the system to round off errors. Two algorithms of preconditioning are presented: the preconditioning algorithm 1 is based on one associated matrix and the preconditioning algorithm 2 is based on two associated matrices. Both algorithms are used in several applications. Each application ends by a test of correctitude of computations, which validates the theory. The solving of models 2 and 3 is done by a general neural network algorithm.
For model 5 a dual quadratic problem (DQP) is associated. The DQP is studied in two cases: for invertible matrix and for non-invertible matrix. In the first case an iterative algorithm is developed ( based on Hildreth and D’ Esopo ideas). Numerical examples illustrate the theory.

Brief Biography of the Speaker:

     Name                        Mr.  Nicolae  POPOVICIU

     Affiliation                 Professor Dr. Math.

                                       HYPERION University of  Bucharest

                                       Dean :  Faculty of  Math. – Info

     Born                         September  4 , 1943

     Place of Born          Romania, District of SIBIU

     Nationality               Romanian

     Religion                   Christian Orthodox

     Married                    1  son

     Education                 Faculty of Mathematics, Diploma  1966

                                        University of Bucharest, Romania

     Doctor in Math        University of Bucharest, Diploma  1976

     Title                           Professor ( full )

     Place of Job             Faculty of Math-Info ( from  2004- today )

                                        Hyperion University of Bucharest, Romania

     Position                    Dean  of  Faculty of  Math-Info

     Published Books    16 ( all in Romanian Language )

     Published Papers   73 ( almost all papers are in English Language )

                                        ( 4 papers are in WSEAS Press )

     Studies Abroad       1970 ( 9 months ) University Lomonosv of Moscow 

                                        1973 ( 6 months ) University Paris VI, France

     Visiting Prof            1977 (1 month ) Technical University of Vienna

                                        1978 ( 2 weeks ) Karolin University of Prague