A partial regularization method for a generalized primal-dual system of inequalities


  • D.A. Dyabilkin
  • I.V. Konnov


generalized primal-dual system
nonmonotone variational inequality
partial regularization method
sufficient convergence conditions


A generalized primal-dual system is considered. The problem is reformulated as an equivalent variational inequality whose main mapping does not possess a monotonicity property and is not the gradient mapping of any function. In order to solve the problem, a partial regularization method is proposed. Its convergence is proved under certain coercitivity-type conditions. An application to an economic equilibrium problem is discussed. The work was supported by the Russian Foundation for Basic Research (project N 10-01-00629).





Section 1. Numerical methods and applications

Author Biographies

D.A. Dyabilkin

I.V. Konnov


  1. Коннов И.В. Двойственный подход для одного класса смешанных вариационных неравенств // Ж. вычисл. матем. и матем. физ. 2002. 42, № 9. 1324-1337.
  2. Konnov I.V. Convex optimization problems with arbitrary right-hand perturbations // Optimization. 2005. 54, N 2. 131-147.
  3. Konnov I.V. Equilibrium models and variational inequalities. Amsterdam: Elsevier, 2007.
  4. Сухарев А.Г., Тимохов А.В., Федоров В.В. Курс методов оптимизации. М.: Наука, 1986.
  5. Дябилкин Д.А., Коннов И.В. Метод частичной регуляризации для немонотонных вариационных неравенств // Ж. вычисл. матем. и матем. физ. 2008. 48, № 3. 355-364.
  6. Hogan W.W. Energy policy models for project independence // Computers and Operations Research. 1975. 2, N 3-4. 251-271.
  7. Ahn B. Computation of market equilibria for policy analysis: the Project Independence Evaluation System (PIES) approach. New York &; London: Garland Publishing, 1979.
  8. Коннов И.В. О сходимости метода регуляризации для вариационных неравенств // Ж. вычисл. матем. и матем. физ. 2006. 46, № 4. 568-575.
  9. Васильев Ф.П. Методы оптимизации. М.: Факториал Пресс, 2002.