• International Journal of Fuzzy Logic and Intelligent Systems
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• 제1권1호
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• pp.35-43
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• 2001

In this paper, we propose a design method for GBSB (generalized brain-state-in-a-box) based associative memories. Based on the theoretical investigation about the properties of GBSB, we parameterize the solution space utilizing the limited number of parameters sufficient to represent the solution space and appropriate to be searched. Next we formulate the problem of finding a GBSB that can store the given pattern as stable states in the form of constrained optimization problems. Finally, we transform the constrained optimization problem into a SDP(semidefinite program), which can be solved by recently developed interior point methods. The applicability of the proposed method is illustrated via design examples.

• Interaction and multiscale mechanics
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• 제1권1호
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• pp.103-121
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• 2008

This paper presents an optimization-based method for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain braced frame. Based on a non-stochastic modeling of uncertainty, we assume that the parameters both of brace stiffnesses and external forces are uncertain but bounded. A brace member represents the sum of the stiffness of the actual brace and the contributions of some non-structural elements, and hence we assume that the axial stiffness of each brace is uncertain. By using the $\mathcal{S}$-lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. The minimum bounding ellipsoids are computed for a braced frame under several uncertain circumstances.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.137-147
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• 2001

Nonconvex Quadratic Optimization Problems (QOP) are solved approximately by SDP (semidefinite programming) relaxation and SOCP (second order cone programmming) relaxation. Nonconvex QOPs with special structures can be solved exactly by SDP and SOCP. We propose a method to formulate general nonconvex QOPs into the special form of the QOP, which can provide a way to find more accurate solutions. Numerical results are shown to illustrate advantages of the proposed method.

• 한국통신학회논문지
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• 제39A권9호
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• pp.519-527
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• 2014

적응 어레이는 조향벡터를 이용하여 조향벡터 방향의 신호는 보호하면서 간섭신호를 제거한다. 조향벡터에 에러가 있으면 원하는 신호도 감쇠되어 SINR(signal-to-interference-plus-noise ratio) 성능 저하를 가져온다. 본 논문에서는 원하는 신호의 도래범위를 이용하여 조향벡터 에러에 강인한 적응 빔 형성 기법을 제시한다. 제시된 기법에서는 도래범위에서 어레이 응답벡터에 관한 상관행렬을 적분을 통해 구하고, 이 상관행렬의 고유벡터 일부를 이용하여 조향벡터를 구하기 위한 최소화 문제를 정의한다. 이 최소화 문제를 컨벡스 최적화(convex optimization)의 일종인 SDP(semidefinite program) 문제로 완화하여 효과적으로 해결한다. 시뮬레이션 결과에 따르면, 제안방식은 기존의 강인한 빔 형성 방식인 ORM(outside-range-based method), USM(uncertainty-based method)보다 우수한 SINR 성능을 나타낸다.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제14권3호
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• pp.162-170
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• 2014

Appearance-based subspace models such as eigenfaces have been widely recognized as one of the most successful approaches to face recognition and tracking. The success of eigenfaces mainly has its origins in the benefits offered by principal component analysis (PCA), the representational power of the underlying generative process for high-dimensional noisy facial image data. The sparse extension of PCA (SPCA) has recently received significant attention in the research community. SPCA functions by imposing sparseness constraints on the eigenvectors, a technique that has been shown to yield more robust solutions in many applications. However, when SPCA is applied to facial images, the time and space complexity of PCA learning becomes a critical issue (e.g., real-time tracking). In this paper, we propose a very fast and scalable greedy forward selection algorithm for SPCA. Unlike a recent semidefinite program-relaxation method that suffers from complex optimization, our approach can process several thousands of data dimensions in reasonable time with little accuracy loss. The effectiveness of our proposed method was demonstrated on real-world face recognition and tracking datasets.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제7권6호
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• pp.1418-1432
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• 2013

This paper studies the problem of secure information exchange between two sources via multiple relays in the presence of an eavesdropper. To this end, we propose a relay beamforming scheme, i.e., relay beamforming with artificial noise (RBwA), where the relay beamforming vector and the artificial noise vector are jointly designed to maintain the received signal-to-interference-ratio (SINR) at the two sources over a predefined Quality of Service (QoS) threshold while limiting the received SINR at the eavesdropper under a predefined secure threshold. For comparison, the relay beamforming without artificial noise (RBoA) is also considered. We formulate two optimization problems for the two schemes, where our goal is to seek the optimal beamforming vector to minimize the total power consumed by relay nodes such that the secrecy of the information exchange between the two sources can be protected. Since both optimization problems are nonconvex, we solve them by semidefinite program (SDP) relaxation theory. Simulation results show that, via beamforming design, physical layer secrecy of two-way relay networks can be greatly improved and our proposed RBwA outperforms the RBoA in terms of both low power consumption and low infeasibility rate.

• Journal of Communications and Networks
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• 제18권2호
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• pp.173-181
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• 2016

In this paper, we address a new robust optimization problem in a multiuser multiple-input single-output broadcasting system with simultaneous wireless information and power transmission, where a multi-antenna base station (BS) sends energy and information simultaneously to multiple users equipped with a single antenna. Assuming that perfect channel-state information (CSI) for all channels is not available at the BS, the uncertainty of the CSI is modeled by an Euclidean ball-shaped uncertainty set. To optimally design transmit beamforming weights and receive power splitting, an average total transmit power minimization problem is investigated subject to the individual harvested power constraint and the received signal-to-interference-plus-noise ratio constraint at each user. Due to the channel uncertainty, the original problem becomes a homogeneous quadratically constrained quadratic problem, which is NP-hard. The original design problem is reformulated to a relaxed semidefinite program, and then two different approaches based on convex programming are proposed, which can be solved efficiently by the interior point algorithm. Numerical results are provided to validate the robustness of the proposed algorithms.