Cyber-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 (primaldual interior point method) and a dichotomy method for search of a global extremum in the general quadratic problems
[1] A. Kosolap, Methods of Global Optimization. Dnipropetrovsk: Science and education, 2013 (in russian).
[2] V. P. Kenneth, R. M. Storn, and J. A. Lampinen, Differential Evolution. A Practical Approach to Global Optimization. Berlin, Heidelberg: Springer-Verlag, 2005.
[3] J. Nocedal, and S.J. Wright, Numerical optimization. Springer, 2006.
[4] Y. Ye, Semidefinite programming. Stanford University, 2003.
[5] 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.
[6] J. Nie, Regularization Methods for Sum of Squares Relaxations in Large Scale Polynomial Optimization. University of California, 2009.
[7] 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.
https://doi.org/10.1007/s10589-014-9637-0
[8] 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.
https://doi.org/10.1007/s101079900106