This paper investigates the physical-layer security of a multiuser peer-to-peer (MUP2P) relay network for amplify-and-forward (AF) protocol, where a secure user and other unclassified users coexist ...with a multi-antenna eavesdropper and the eavesdropper can wiretap the confidential information in both two cooperative phases. Our goal is to optimize the transmit power of the source and the beamforming weights of the relays jointly for secrecy rate maximization subject to the minimum signal-to-interference-noise-ratio (SINR) constraint at each user, and the individual and total power constraints. Mathematically, the optimization problem is non-linear and non-convex, which does not facilitate an efficient resource allocation algorithm design. As an alternative, a null space beamforming scheme is adopted at the relays for simplifying the joint optimization and eliminating the confidential information leakage in the second cooperative phase, where the relay beamforming vector lies in the null space of the equivalent channel of the relay to eavesdropper links. Although the null space beamforming scheme simplifies the design of resource allocation algorithm, the considered problem is still non-convex and obtaining the global optimum is very difficult, if not impossible. Employing a sequential parametric convex approximation (SPCA) method, we propose an iterative algorithm to obtain an efficient solution of the non-convex problem. Besides, the proposed joint design algorithm requires a feasible starting point, we also propose a low complexity feasible initial points searching algorithm. Simulations demonstrate the validity of the proposed strategy.
•An efficient multiple meta-model-based global optimization (EMMGO) algorithm is developed.•The design space is divided into an important region and a remaining region: 21 new trial points are ...selected in each iteration.•Multiple searches improve efficiency and robustness of the search process•EMMGO outperforms other state-of-the-art algorithms in six mathematical optimization problems and a real structural optimization problem.
Present metamodel based global optimization algorithms usually build an evolving metamodel using initial and updated sample points to speed up the search of the global optimum. In this research, we proposed an efficient and robust multiple meta-model-based global optimization method (EMMGO). The EMMGO starts with two different sets of initial points and two different sets of evolving metamodels to search the design space. One evolving set of meta-models are updated using all sample points at each iteration of the search. The other set of meta-models are constructed using the sample points without the set of points which contains the initial best. These two sets of evolving meta-models consist of three components: radial basis function, Kriging and quadratic function. In the iterative search process, an important region, likely to contain the global optimum, is first identified using a few expensive points, and the search of the global optimum is conducted over this region using both of the two sets of metamodels. Meanwhile, the evolving meta-models fitted using all obtained points are used in the search over the other area and the entire design space to avoid missing the global optimum. The new EMMGO algorithm is tested using several commonly-used benchmark functions. The search efficiency of the new algorithm is also illustrated by solving a practical, computationally intensive global optimization problem in designing a lightweight vehicle, employing finite element analysis and simulation. The results from efficient global optimization and multiple metamodels based design space differentiation are provided for search performance comparison.
In this work, a hybrid meta-model-based global optimum pursuing (HMGOP) method is proposed for the expensive practical problems. In this method, a so-called important region is constructed using ...several expensive points. Three representative meta-models will then be used in both the important region and remaining region. A strategy to leave enough space for the remaining region has also been proposed to avoid the undesired points due to the narrow remaining region. The search process in the whole design space will also be carried out to further demonstrate the global optimum. Through test by several two-dimensional (2D) functions, each of which having several local optima, the proposed method shows great ability to escape the trap of the local optima. Through test with six high-dimensional problems, the proposed HMGOP method shows excellent search accuracy, efficiency, and robustness. Then, the proposed HMGOP method is applied in a vehicle lightweight design with 30 design variables, achieving satisfied results.
The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial ...points of the realization. Several examples, as the HJMM equation from mathematical finance, illustrate our results.
As one of the most popular clustering algorithms, k-means is easily influenced by initial points and the number of clusters, besides, the iterative class center calculated by the mean of all points ...in a cluster is one of the reasons influencing clustering performance. Representational initial points are selected in this paper according to the decision graph composed by local density and distance of each point. Then we propose an improved k-means text clustering algorithm, the iterative class center of the improved algorithm is composed by subject feature vector which can avoid the influence caused by noises. Experiments show that the initial points are selected successfully and the clustering results improve 3%, 5%, 2% and 7% respectively than traditional k-means clustering algorithm on four experimental corpuses of Fudan and Sougou.
In this paper, a boundary perturbation interior point homotopy method is proposed to give a constructive proof of the general Brouwer fixed point theorem and thus solve fixed point problems in a ...class of nonconvex sets. Compared with the previous results, by using the newly proposed method, initial points can be chosen in the whole space of Rn, which may improve greatly the computational efficiency of reduced predictor–corrector algorithms resulted from that method. Some numerical examples are given to illustrate the results of this paper.
Constraint-reduction schemes have been proposed for the solution by means of interior-point methods of linear programs with many more inequality constraints than variables in the standard dual form. ...Such schemes have been shown to be provably convergent and highly efficient in practice. A critical requirement of these schemes is the availability of an initial dual-feasible point.
In this paper, building on a general framework (which encompasses several previously proposed approaches) for dual-feasible constraint-reduced interior-point optimization, for which we prove convergence to a single point of the sequence of dual iterates, we propose a framework for 'infeasible' constraint-reduced interior-point optimization. Central to this framework is an exact (ℓ
1
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) penalty function scheme endowed with a mechanism for iterative adjustment of the penalty parameter, which aims at yielding, after a finite number of iterations, a value that guarantees feasibility (for the original problem) of the minimizers. Finiteness of the sequence of penalty parameter adjustments is proved under mild assumptions for all algorithms that fit within the framework, including 'infeasible' extensions of a 'dual' algorithm proposed in the early 1990s (Dantzig and Ye, A build-up interior-point method for linear programming: Affine scaling form, Working paper, Department of Management Science, University of Iowa, 1991) and of two recently proposed 'primal-dual' algorithms (Tits, Absil, and Woessner, Constraint reduction for linear programs with many inequality constraints, SIAM J. Optim. 17 (2006), pp. 119-146; Winternitz, Nicholls, Tits, and O'Leary, A constraint-reduced variant of Mehrotra's predictor-corrector algorithm, Comput. Optim. Appl. (published on-line as of January 2011), DOI: 10.1007/s10589-010-9389-4). The last one, a constraint-reduced variant of Mehrotra's Predictor-Corrector algorithm, is then more specifically considered: further convergence results are proved, and numerical results are reported that demonstrate that the approach is of practical interest.
Clustering is considered one of the most powerful tools for analyzing gene expression data. Although clustering has been extensively studied, a problem remains significant: iterative techniques like ...k-means clustering are especially sensitive to initial starting conditions. An unreasonable selection of initial points leads to problems including local minima and massive computation. In this paper, a spatial contiguity analysis-based approach is proposed, aiming to solve this problem. It employs principal component analysis (PCA) to identify data points that are likely extracted from different clusters as initial points. This helps to avoid local minima, and accelerates the computation. The effectiveness of the proposed approach was validated on several benchmark datasets.
This work proposes a robust fully automatic segmentation scheme based on the modified edge-following technique. The entire scheme consists of four stages. In the first stage, global threshold is ...computed. This is followed by the second stage in which positions and directions of the initial points are determined. Local threshold is derived based on the histogram of gradients from the third stage. Finally, in the fourth stage, searching procedure is started from each initial point to obtain closed-loop contours. The whole process is fully automatic. This avoids the disadvantages of semi-automatic schemes such as manually selecting the initial contours and points. Additionally, the sensitivity to the selection of the threshold value from the watershed schemes can be dramatically improved. The proposed automatic scheme can reduce human errors and operating time tremendously, it is also more robust than the conventional segmentation schemes and applicable on various image and video applications.
In this paper, by introducing
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and using the idea of the aggregate function method, a new aggregate constraint homotopy method is proposed to solve the ...Karush–Kuhn–Tucker (KKT) point of nonconvex nonlinear programming problems. Compared with the previous results, the choice scope of initial points is greatly enlarged, so use of the new aggregate constraint homotopy method may improve the computational efficiency of reduced predictor–corrector algorithms.
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