Vladimir K Gorbunov

My scientific career began in 1970 at Tashkent State University, where I worked as junior scientist, senior scientist, senior lecturer until 1976. This period my scientific works were fulfilled as the postgraduate program (in absentia form, under scientific leadership by professor Chernous’ko F.L.), and its developing. They were devoted to mathematical problems of optimization of dynamic systems with mixed discrete-continuous control (particularly in antagonistic way, that I called the differential-impulse games), and to some applied investigations. The first scientific degree of the Candidate of physical-mathematical sciences (analogue of PhD) I obtained in 1974 (MPhTI).

The second period (1976-1990) has passed in the Mathematics Institute of Kyrgyzstan Academy of Sciences. There I had occupied posts of senior scientist and later the head of laboratory. I started investigation in area of irregular (in different senses) problems of the theory of differential and integral (at first ordinary) equations, optimization and modeling of demographic processes [The system analysis of economic and demographic growth, in USSR Academy of Sciences Communications: Technical Cybernetics, 1981 (1) 32-38 (in Russian)].

Main results of the second period are: the parameterization method for optimal control problems [1] (work from the list below), the normal splines (NS) [2, 3], the extended minimization for regularization of equations and extremum problems [2, 4]. The NS method is the first numerical method based on the canonical transformation of linear bounded functionals in Hilbert spaces of Sobolev type to the inner product form, i.e. constructive usage of the classical Riesz representation theorem. Now this approach [2, 3] (the first reported by me on the ICM-82, Warsaw) is actively developing by many western authors as Reproducing Kernel Hilbert Space method (without references to my priority). These results were the basis of my doctorate dissertation (Dr. Sci.). “Extremum problems of processing of experiment measurements’ results”, defended at 1991 in Computer Center of Siberian Branch of the USSR Ac. Sci., Novosibirsk.

Since 1990, I work for the Ulyanovsk State University. My position from 1992 was Professor of Applied Mathematics Chair, and from 2002 is the Head of the Chair of Mathematical Economics. I continue investigations in the field of singular and ill-posed problems of differential and integral equations [5, 6, 7, 8, 10], and in modeling of the consumer demand [9]. My last result is the generalized model of the consumer demand without utility function. The consumer preferences in my model can be non-complete and non-transitive. At the same time almost all analytical properties of the classical model are kept.