Singular optimal regimes in problems of mathematical economics
This paper consists of two chapters, focusing on singular extremals and their role in the construction of optimal syntheses. Economical interpretations are given for the results obtained. The approach in finding singular extremals is based on the method of differential forms. An optimality condition for finding singular extremals is proved, which is thought to be more effective than the results obtained via the classical calculus of variations. Theorems with applications in Economy, among which the attractor theorem for first-order singular regimes and various theorems on the structure of optimal synthesis in a neighborhood of singular regimes, are translated in the language of differential forms and then proved. The second chapter is devoted to second order singular trajectories and nonsingular extremals with accumulation of switchings. The authors introduce and discuss here basic concepts of switching accumulation regimes, such as the theorem on the existence of a bundle containing trajectories with switching accumulation, the theorem on the Lagrangian submanifold, sufficient optimality conditions for this regime, or the attractor theorem. The presentation is accompanied by many examples and problems, together with their detailed solutions.
scientific article; zbMATH DE number 5000638
scientific article