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For globally solving sum of linear ratios problem (SLRP), this paper presents a new branch-and-bound method. In this method, a new linear relaxation technique is proposed firstly; then, the initial problem SLRP is solved by a sequence of linear programming problems. Meanwhile, to improve the convergence speed of our algorithm, two accelerating techniques are presented. The proposed algorithm is proved to be convergent, and some experiments are provided to show its feasibility and efficiency. [ABSTRACT FROM AUTHOR]

In this paper, for solving generalized linear fractional programming (GLFP), a new branch-and-reduce approach is presented. Firstly, an equivalent problem (EP) of GLFP is given; then, a new linear relaxation technique is proposed; finally, the problem EP is reduced to a sequence of linear programming problems by using the new linear relaxation technique. Meanwhile, to improve the convergence speed of our algorithm, two reducing techniques are presented. The proposed algorithm is proved to be convergent, and some experiments are provided to show its feasibility and efficiency. [ABSTRACT FROM AUTHOR]

In recent years, progress has been made in the analysis of global convergence of clonal selection algorithms (CSA), but most analyses are based on the theory of Markov chain, which depend on the description of the transition matrix and eigenvalues. However, such analyses are very complicated, especially when the population size is large, and are presented for particular implementations of CSA. In this paper, instead of the traditional Markov chain theory, we introduce martingale theory to prove the convergence of a class of CSA, called elitist clonal selection algorithm (ECSA). Using the submartingale convergence theorem, the best individual affinity evolutionary sequence is described as a submartingale, and the almost everywhere convergence of ECSA is derived. Particularly, the algorithm is proved convergent with probability 1 in finite steps when the state space of population is finite. This new proof of global convergence analysis of ECSA is more simplified and effective, and not implementation specific. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new algorithm M-SMFTF for adaptive filtering with fast convergence and low complexity. It is the result of a simplified FTF type algorithm, where the adaptation gain is obtained only from the forward prediction variables and using a new recursive method to compute the likelihood variable. The computational complexity was reduced from 7L to 6L, where L is the finite impulse response filter length. Furthermore, this computational complexity can be significantly reduced to (2L+4P) when used with a reduced P-size forward predictor. This algorithm presents a certain interest, for the adaptation of very long filters, like those used in the problems of echo acoustic cancellation, due to its reduced complexity, its numerical stability and its convergence in the presence of the speech signal. The proposed algorithm outperforms the classical adaptive algorithms because of its convergence speed which approaches that of the RLS algorithm and its computational complexity which is slightly greater than the one of the normalized LMS algorithm. [ABSTRACT FROM AUTHOR]

Nonlinear inter-symbol interference leads to significant error rate in nonlinear communication and digital storage channel. In this paper, therefore, a novel recurrent interval type-2 fuzzy neural network with asymmetric membership functions (RT2FNN-A) is proposed for nonlinear channel equalization. The RT2FNN-A uses the interval asymmetric type-2 fuzzy sets and it implements the fuzzy logic system in a five-layer neural network structure. The RT2FNN-A is an extensive results of type-2 fuzzy neural network to provide memory elements for capturing the system's dynamic information and has the properties of high approximation accuracy and small network structure. Based on the Lyapunov theorem and gradient descent method, the convergence of RT2FNN-A is guaranteed and the corresponding learning algorithm is derived. In addition, the RT2FNN-A is applied in the nonlinear channel equalization to show the performance and effectiveness of RT2FNN-A system. [ABSTRACT FROM AUTHOR]