Достатня умова точної двоїстої оцінки для сепарабельної квадратичної оптимізаційної задачі: Fìz.-mat. model. ìnf. tehnol. 2021, 32:42-45

• Date: 2021
• Main Author: Berezovskyi, Oleg
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Subjects: сепарабельна квадратична оптимізаційна задача; глобальний екстремум; двоїста оцінка; додатно визначена матриця; нульовий розрив двоїстості
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/157
• Journal Title: Physico-mathematical modeling and informational technologies

The paper considers nonconvex separable quadratic optimization problems subject to inequality constraints. A sufficient condition is given for finding the value and the point of the global extremum of a problem of this type by calculating the Lagrange dual bound. The peculiarity of this condition is that it is easily verified and requires from the Hessian matrix of the Lagrange function only that its region of positive definiteness is not empty. The result obtained for the dual bound also holds for the bound obtained using SDP relaxation. References Shor, N. Z., Stetsenko, S. I. (1989). Quadratic extremal problems and nondifferentiable optimization. Naukova Dumka, Kiev. Berezovskyi, O. A. (2017). Zero duality gap in quadratically constrained quadratic programming. Mathematical and computer modelling. Series: Physical and mathematical sciences, 15, 20-25. Nesterov, Y., Wolkowicz, H., Ye, Y. (2000). Semidefinite programming relaxations of nonconvex quadratic optimization. Handbook of semidefinite programming, Springer, New York, 361-419. DOI doi.org/10.1007/978-1-4615-4381-7_13 Berezovskyi, O. A. (2016). Exactness criteria for SDP-relaxations of quadratic extremum problems. Cybernetics and Systems Analysis, 52(6), 915-920. DOI doi.org/10.1007/s10559-016-9893-3