Generalized Concavity

Avriel, Mordecai; Diewert, W. Erwin; Schaible, Siegfried; Zang, Israël

doi:10.1007/978-1-4684-7600-2_3

Cited by 41 publications

(60 citation statements)

References 21 publications

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“…In contrast to the channel-diagonalization methods 78 of [9], [10] systems. Additionally, the Charnes-Cooper transformation [24] 120 is employed in this paper for solving the associated ESEM 121 problem, in contrast to the scalarization approach [25] [8]. Although these locally orthogonal rows may not remain 337 orthogonal globally, they can be characterized using the semi-338 orthogonality metric of (1).…”

Section: E E E P R O O Fmentioning

confidence: 99%

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Spectral and Energy Spectral Efficiency Optimization of Joint Transmit and Receive Beamforming Based Multi-Relay MIMO-OFDMA Cellular Networks

Cheung

Yang²,

Hanzo³

2014

IEEE Trans. Wireless Commun.

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Section: E E E P R O O Fmentioning

confidence: 99%

“…Thus the ESEM prob-764 lem can be solved using the Charnes-Cooper transformation of 765 [24], as given by…”

mentioning

confidence: 99%

Spectral and Energy Spectral Efficiency Optimization of Joint Transmit and Receive Beamforming Based Multi-Relay MIMO-OFDMA Cellular Networks

Cheung

Yang²,

Hanzo³

2014

IEEE Trans. Wireless Commun.

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“…It is well known (e.g., Avriel et al, 1988) that f is pseudoconvex on X when Q ≥ 0. Conditions for f being pseudoconvex on X when Q is not positive semidefinite are discussed in (Cambini et al, 2002).…”

Section: Solving Pseudoconvex Optimization Problemsmentioning

confidence: 99%

Neurodynamic Optimization: towards Nonconvexity

Hu¹

2008

Recurrent Neural Networks

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“…Although the objective function of (1.1) is not concave but pseudoconcave [2]. we can reduce it to a concave minimization problem by introducing a vector x = (x 1 , .…”

Section: Introductionmentioning

confidence: 99%

A simplicial branch-and-bound algorithm conscious of special structures in concave minimization problems

Kuno

Nagai

2007

Comput Optim Appl

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In this paper, we develop a simplicial branch-and-bound algorithm for generating globally optimal solutions to concave minimization problems with low rank nonconvex structures. We propose to remove all additional constraints imposed on the usual linear programming relaxed problem. Therefore, in each bounding operation, we solve a linear programming problem whose constraints are exactly the same as the target problem. Although the lower bound worsens as a natural consequence, we offset this weakness by using an inexpensive bound tightening procedure based on Lagrangian relaxation. After giving a proof of the convergence, we report a numerical comparison with existing algorithms.

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Generalized Concavity

Cited by 41 publications

References 21 publications

Spectral and Energy Spectral Efficiency Optimization of Joint Transmit and Receive Beamforming Based Multi-Relay MIMO-OFDMA Cellular Networks

Spectral and Energy Spectral Efficiency Optimization of Joint Transmit and Receive Beamforming Based Multi-Relay MIMO-OFDMA Cellular Networks

Neurodynamic Optimization: towards Nonconvexity

A simplicial branch-and-bound algorithm conscious of special structures in concave minimization problems

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