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• W2007104311 abstract "In this paper we study the approximation algorithms for a class of discrete quadratic optimization problems in the Hermitian complex form. A special case of the problem that we study corresponds to the max-3-cut model used in a recent paper of Goemans and Williamson J. Comput. System Sci., 68 (2004), pp. 442-470]. We first develop a closed-formformula to compute the probability of a complex-valued normally distributed bivariate random vector to be in a given angular region. This formula allows us to compute the expected value of a randomized (with a specific rounding rule) solution based on the optimal solution of the complex semidefinite programming relaxation problem. In particular, we present an $[m^2(1-cosfrac{2pi}{m})/8pi]$-approximation algorithm, and then study the limit of that model, in which the problem remains NP-hard. We show that if the objective is to maximize a positive semidefinite Hermitian form, then the randomization-rounding procedure guarantees a worst-case performance ratio of $pi/4 approx 0.7854$, which is better than the ratio of $2/pi approx 0.6366$ for its counterpart in the real case due to Nesterov. Furthermore, if the objective matrix is real-valued positive semidefinite with nonpositive off-diagonal elements, then the performance ratio improves to 0.9349." @default.
• W2007104311 created "2016-06-24" @default.
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• W2007104311 date "2006-01-01" @default.
• W2007104311 modified "2023-09-29" @default.
• W2007104311 title "Complex Quadratic Optimization and Semidefinite Programming" @default.
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• W2007104311 doi "https://doi.org/10.1137/04061341x" @default.
• W2007104311 hasPublicationYear "2006" @default.
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