Improving the efficiency of DC global optimization methods by improving the DC representation of the objective function

Ferrer, Albert; Martínez-Legaz, Juan Enrique

doi:10.1007/s10898-008-9343-5

Cited by 13 publications

(9 citation statements)

References 11 publications

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“…is an explicit DC function, and problem (25) can be solved by DC algorithms. However, this DC representation is not efficient because k is too large [32]. Through extensive simulations, we observe that even when each node in the system is only equipped with two antennas, the DC algorithm with this representation cannot converge within hundreds of thousands of iterations.…”

Section: A Precoder Vectorizationmentioning

confidence: 99%

“…However, no practical algorithm is known to construct a DC decomposition for arbitrary twice continuously differentiable function. Moreover, if we do not carefully design the DC representation of the average secrecy sum rate, the algorithms in [29]- [31] suffer from very slow convergence [32]. Therefore, the DC representation is a main factor that affect the performance of DC algorithms.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Linear Precoding for Fading Cognitive Multiple-Access Wiretap Channel With Finite-Alphabet Inputs

Jun-ze

Xiao

Tao

et al. 2017

IEEE Trans. Veh. Technol.

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We investigate the fading cognitive multiple access wiretap channel (CMAC-WT), in which two secondary-user transmitters (STs) send secure messages to a secondary-user receiver (SR) in the presence of an eavesdropper (ED) and subject to interference threshold constraints at multiple primaryuser receivers (PRs). We design linear precoders to maximize the average secrecy sum rate for multiple-input multiple-output (MIMO) fading CMAC-WT under finite-alphabet inputs and statistical channel state information (CSI) at STs. For this nondeterministic polynomial time (NP)-hard problem, we utilize an accurate approximation of the average secrecy sum rate to reduce the computational complexity, and then present a two-layer algorithm by embedding the convex-concave procedure into an outer approximation framework. The idea behind this algorithm is to reformulate the approximated average secrecy sum rate as a difference of convex functions, and then generate a sequence of simpler relaxed sets to approach the non-convex feasible set. Subsequently, we maximize the approximated average secrecy sum rate over the sequence of relaxed sets by using the convexconcave procedure. Numerical results indicate that our proposed precoding algorithm is superior to the conventional Gaussian precoding method in the medium and high signal-to-noise ratio (SNR) regimes.Index Terms-Finite-alphabet inputs, linear precoding, MIMO, statistical CSI, physical-layer security, cognitive multiple access wiretap channel.

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Section: A Precoder Vectorizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Linear Precoding for Fading Cognitive Multiple-Access Wiretap Channel With Finite-Alphabet Inputs

Jun-ze

Xiao

Tao

et al. 2017

IEEE Trans. Veh. Technol.

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“…One example is polynomials for which special algorithms are presented to determine the best DC decomposition [1,19,37]. In addition, a special norm minimization problem is presented in [38] to improve the DC representation mainly in the polynomial case.…”

Section: Functionmentioning

confidence: 99%

Bundle Methods for Nonsmooth DC Optimization

Joki

Bagirov

2020

Numerical Nonsmooth Optimization

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Due to the complexity of many practical applications, we encounter optimization problems with nonsmooth functions, that is, functions which are not continuously differentiable everywhere. Classical gradient-based methods are not applicable to solve such problems, since they may fail in the nonsmooth setting. Therefore, it is imperative to develop numerical methods specifically designed for nonsmooth optimization. To date, bundle methods are considered to be the most efficient and reliable general purpose solvers for this type of problems.

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“…Thus, the Difference of Convex Algorithm (DCA) is a suitable tool to find good quality solutions which requires a DC decomposition of the objective function. The performance of the DCA strongly depends on the choice of the DC decomposition, [10,11,28]. In this work, as in [18,39,53], we seek a DC decomposition of F , with fixed x, whose expression is formed by a quadratic separable convex function minus a convex function, as stated in Proposition 1.…”

Section: Accepted Manuscriptmentioning

confidence: 99%