Cybernetics and Systems Analysis

, Volume 53, Issue 5, pp 712–724 | Cite as

Using Conical Regularization in Calculating Lagrangian Estimates in Quadratic Optimization Problems

  • Yu. P. LaptinEmail author
  • O. A. Berezovskyi


For nonconvex quadratic optimization problems, the authors consider calculation of global extreme value estimates on the basis of Lagrangian relaxation of the original problems. On the boundary of the feasible region of the estimate problem, functions of the problem are discontinuous, ill-conditioned, which imposes certain requirements on the computational algorithms. The paper presents a new approach taking into account these features, based on the use of conical regularizations of convex optimization problems. It makes it possible to construct an equivalent unconditional optimization problem whose objective function is defined on the entire space of problem variables and satisfies the Lipschitz condition.


quadratic optimization problem Lagrangian relaxation condition of nonnegative definiteness of matrix conical regularization 


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

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