National Academy of Sciences of Belarus

GOROKHOVIK Valentin Vikentevich

Valentin Vikentevich Gorokhovik (b. 29.03.1949, v. Khoroshee, Logoisk district, Minsk region), mathematician. Corresponding Member of the National Academy of Sciences of Belarus (2000). Doctor of Physico-Mathematical Sciences (1989), Professor (1991).

Scientific works in the field of nonlinear analysis and mathematical theory of optimization. He developed the mathematical foundations of the theory of vector optimization. He introduced linear and convex analysis of step-linear and step-affine functions and developed the theory of separability of convex sets by step-affine functions, which generalizes the classical theory of separability of convex sets by hyperplanes. As an application of this theory, he proposed a new approach to the study of convex optimization problems, based on the separability of convex sets by step-affine functions. Received criteria for optimality of solutions in convex vector optimization problems and in non-regular classical convex programming problems. He developed the theory of polyhedral and approximate quasidifferentiation. Applying the developed technique of polyhedral and approximate quasidifferentiation to the study of general vector optimization problems and optimal control problems according to the vector quality indicator, he developed for them a theory of necessary and sufficient conditions of optimality of the first and higher orders. In a multivalued analysis, the main results are connected with the differentiability of multivalued mappings and with the extension to the multivalued mappings of the classical notion of Fréchet differentiability. In the framework of the theory of differentiation of multivalued mappings, carried out research on affine multivalued mappings.

Author of more than 100 scientific papers, including monographs and textbooks.

Major papers:

  1. Выпуклые и негладкие задачи векторной оптимизации. Мн.: Навука i тэхнiка, 1990.
  2. Piecewise affine functions and polyhedral sets (в соавт. с О.И.Зорько) // Optimization. 1994. Vol.31, №2.
  3. Geometric structure and classification of infinite-dimensional halfspaces (в соавт. с Е.А.Шинкевич) // Algebraic Analysis and Related Topics / Banach Center Publications. 2000. Vol.53.
  4. Конечномерные задачи оптимизации. Мн.: Издат. центр БГУ, 2007.