Abstract: Many science and engineering problems can be formulated as optimization problems that are governed by contact distributions (multi-time Pfaff evolution systems)
and by cost functionals expressed as multiple integrals or curvilinear integrals. Our paper discuss the contact distribution constrained optimization problems, focussing on a geometric approach of multi-time maximum principle. This extends the work of Pontryaguin in the ODEs case to include the case of normal PDEs or, more general, the distribution case.

Section 1 formulates and proves a multi-time maximum principle for the case of multiple integral functionals. Section 2 establishes a version of multi-time maximum principle for the case of curvilinear integral functionals. Though a multiple integral functional is mathematically equivalent to a curvilinear integral functional (Section 3), their meaning is totally different in real life problems. Section 4 deals with a multi-time maximum principle approach of variational calculus in the case of nonintegrability.

 

Brief Biography of the Speaker:

Important Career Positions: Dean, Director, Chair, Full Professor 1990-, University Politehnica of Bucharest, Department of Mathematics.

Number of PhD Students: 25 in due time and 13 Doctors in Mathematics.

Membership of Associations: AMS, 1987; Tensor Society, 1985; Balkan Society of Geometers, President, 1994;

Publications: over 40 books; 200 papers; 200 communications.

Honors: D. Hurmuzescu Prize, Romanian Academy, 1985; Award MEI, 1988; Correspondent Member, Academia Peloritana, Messina, 1997; Titular Member, Academy of Romanian Scientists, 2007; Honorary Member, World Scientific and Engineering Academy and Society, 2008-;

Organizer: The International Conference of Differential Geometry and Dynamical Systems, University Politehnica of Bucharest, October 5-7, 2007; 7th WSEAS International Conference on Systems Theory and Scientific Computation (ISTASC'07), Vouliagmeni Beach, Athens, Greece, August 24-26 (2007); European Computing Conference, Vouliagmeni Beach, Athens, Greece, September 24-26, 2007; 12th WSEAS International Conference on Applied Mathematics, Cairo, Egypt, Dec. 29-31, 2007; 7th WSEAS International Conference on Circuits, Systems, Electronics, Control and Signal Processing, Cairo, Egypt, Dec. 29-31, 2007; Chair-Committee: American Conference on Applied Mathematics (Math’08) and Management, Marketing and Finances (MMF’08), Cambridge, Massachusetts, USA, March 24-26, 2008; International Program Committee: The Applied Computing Conference (ACC-08), Istanbul, Turkey, May 27-30, 2008.

Fields of Interest: Differential Geometry, Optimizations on Riemannian Manifolds, Magnetic Dynamical Systems, Geometric Dynamics.