Plenary lecture I: geometrical approach of multi-time maximum principle
Constantin Udrişte · International Conference on Mathematical methods, Computational techniques and Intelligent systems · 2008
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.