Finding the global minimum of the general quadratic problems during deterministic global optimization in Cyber-Physical Systems

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dc.citation.epage35
dc.citation.issue1
dc.citation.spage31
dc.citation.volume4
dc.contributor.affiliationUniversity of Chemical Engineering, Dnipro
dc.contributor.authorKosolap, Anatolii
dc.coverage.placenameЛьвів
dc.date.accessioned2020-02-18T08:58:36Z
dc.date.available2020-02-18T08:58:36Z
dc.date.created2019-02-26
dc.date.issued2019-02-26
dc.description.abstractCyber-Physical Systems (CPS) are integrations of computation and physical processes. We consider effective computations for designing difficult systems. In this paper, we propose new method of exact quadratic regularization for deterministic global optimization (EQR). This method can be used for the solution of a wide class of multiextreme problems, in particular, general quadratic problems. These problems will be transformed to maximization of norm a vector on convex set. The convex set is approximated by a polyhedron or intersection of balls. We offer the modified dual problem for maximization of norm a vector on intersection of balls. It allows to receive the solution of a primal problem. We use only local search (primal-dual interior point method) and a dichotomy method for search of a global extremum in the general quadratic problems.
dc.format.extent31-35
dc.format.pages5
dc.identifier.citationKosolap A. Finding the global minimum of the general quadratic problems during deterministic global optimization in Cyber-Physical Systems / Anatolii Kosolap // Advances in Cyber-Physical Systems : scientific journal. — Львів : Lviv Politechnic Publishing House, 2019. — Vol 4. — No 1. — P. 31–35.
dc.identifier.citationenKosolap A. Finding the global minimum of the general quadratic problems during deterministic global optimization in Cyber-Physical Systems / Anatolii Kosolap // Advances in Cyber-Physical Systems : scientific journal. — Lviv Politechnic Publishing House, 2019. — Vol 4. — No 1. — P. 31–35.
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/45648
dc.language.isoen
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofAdvances in Cyber-Physical Systems : scientific journal, 1 (4), 2019
dc.relation.references1. A. Kosolap, Methods of Global Optimization. Dnipropetrovsk: Science and education, 2013 (in russian).
dc.relation.references2. V. P. Kenneth, R. M. Storn, and J. A. Lampinen, Differential Evolution. A Practical Approach to Global Optimization. Berlin, Heidelberg: Springer-Verlag, 2005.
dc.relation.references3. J. Nocedal, and S.J. Wright, Numerical optimization. Springer, 2006.
dc.relation.references4. Y. Ye, Semidefinite programming. Stanford University, 2003.
dc.relation.references5. A. P. Piotrowski and J. J. Napiórkowski, (2010) The grouping dierential evolution algorithm for multi-dimensional optimization problems. Control and Cybernetics, vol. 39, No. 2, pp. 527–550.
dc.relation.references6. J. Nie, Regularization Methods for Sum of Squares Relaxations in Large Scale Polynomial Optimization. University of California, 2009.
dc.relation.references7. M. K. Dhadwal, S. N. Jung, C. J. Kim, (2014) Advanced particle swarm assisted genetic algorithm for constrained optimization problems. Comput. Optim. Appl., 58, pp. 781–806.
dc.relation.references8. C. Audet, P. Hansen, B. Jaumard, G. Savard, (2000) A branch and cut algorithm for nonconvex quadratically constrained quadratic programming. Math. Program., Ser. A 87, pp. 131–152.
dc.relation.referencesen1. A. Kosolap, Methods of Global Optimization. Dnipropetrovsk: Science and education, 2013 (in russian).
dc.relation.referencesen2. V. P. Kenneth, R. M. Storn, and J. A. Lampinen, Differential Evolution. A Practical Approach to Global Optimization. Berlin, Heidelberg: Springer-Verlag, 2005.
dc.relation.referencesen3. J. Nocedal, and S.J. Wright, Numerical optimization. Springer, 2006.
dc.relation.referencesen4. Y. Ye, Semidefinite programming. Stanford University, 2003.
dc.relation.referencesen5. A. P. Piotrowski and J. J. Napiórkowski, (2010) The grouping dierential evolution algorithm for multi-dimensional optimization problems. Control and Cybernetics, vol. 39, No. 2, pp. 527–550.
dc.relation.referencesen6. J. Nie, Regularization Methods for Sum of Squares Relaxations in Large Scale Polynomial Optimization. University of California, 2009.
dc.relation.referencesen7. M. K. Dhadwal, S. N. Jung, C. J. Kim, (2014) Advanced particle swarm assisted genetic algorithm for constrained optimization problems. Comput. Optim. Appl., 58, pp. 781–806.
dc.relation.referencesen8. C. Audet, P. Hansen, B. Jaumard, G. Savard, (2000) A branch and cut algorithm for nonconvex quadratically constrained quadratic programming. Math. Program., Ser. A 87, pp. 131–152.
dc.rights.holder© Національний університет “Львівська політехніка”, 2019
dc.rights.holder© Kosolap A., 2019
dc.subjectglobal optimization
dc.subjectexact quadratic regularization
dc.subjectgeneral quadratic problems
dc.subjectintersection of balls
dc.subjectmodified dual theory
dc.subjecttest problems
dc.titleFinding the global minimum of the general quadratic problems during deterministic global optimization in Cyber-Physical Systems
dc.typeArticle

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Advances In Cyber-Physical Systems. – 2019. – Vol. 4, No. 1