In this paper, the efficient hinging hyperplanes (EHH) neural network is proposed based on the model of hinging hyperplanes (HH). The EHH neural network is a distributed representation, the training of which involves solving several convex optimization problems and is fast. It is proved that for every EHH neural network, there is an equivalent adaptive hinging hyperplanes (AHH) tree, which was also proposed based on the model of HH and find good applications in system identification. The construction of the EHH neural network includes 2 stages. First the initial structure of the EHH neural network is randomly determined and the Lasso regression is used to choose the appropriate network. To alleviate the impact of randomness, secondly, the stacking strategy is employed to formulate a more general network structure. Different from other neural networks, the EHH neural network has interpretability ability, which can be easily obtained through its ANOVA decomposition (or interaction matrix). The interpretability can then be used as a suggestion for input variable selection. The EHH neural network is applied in nonlinear system identification, the simulation results show that the regression vector selected is reasonable and the identification speed is fast, while at the same time, the simulation accuracy is satisfactory.

In this paper, the portfolio selection problem under Cumulative Prospect Theory (CPT) is investigated and a model of portfolio optimization is presented. This model is solved by coupling scenario generation techniques with a genetic algorithm. Moreover, an Adaptive Real-Coded Genetic Algorithm (ARCGA) is developed to find the optimal solution for the proposed model. Computational results show that the proposed method solves the portfolio selection model and that ARCGA is an effective and stable algorithm. We compare the portfolio choices of CPT investors based on various bootstrap techniques for scenario generation and empirically examine the effect of reference points on investment behavior.

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In order to recover a signal from its compressive measurements, the compressed sensing theory seeks the sparsest signal that agrees with the measurements, which is actually an l 0 norm minimization problem. In this paper, we equivalently transform the l 0 norm minimization into a concave continuous piecewise linear programming, and propose an optimization algorithm based on a modified interior point method. Numerical experiments demonstrate that our algorithm improves the sufficient number of measurements, relaxes the restrictions of the sensing matrix to some extent, and performs robustly in the noisy scenarios.

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This paper describes continuous piecewise linear (CPWL) programming where the objective and constraints are in the form of hinging hyperplane (HH). And HH has received wide attention due to its simplicity and good performance in system identification. When solving a CPWL programming problem, some excellent features inspire us to come up with more efficient algorithms: the two distinguished states of a hinge function reminds us of application of genetic algorithm, while the piecewise linearity and concavity of the problem of minimization of HH naturally lead to the usage of well developed methods for concave programming, such as the cutting plane method. In order to find the global minima, we propose an improved genetic algorithm (GA) incorporating the cutting plane method. The main improvement lies in three aspects. First, it utilizes binary strings that derive local minima as chromosomes, with the proposed local minima locating method. Second, a stopping criterion has been established to ensure the global optimality of GA, with the structure information provided by γ extension of local minima. And third, genetic operations have also been revised to enhance the performance of the algorithm, which is assessed by the computational experiments.

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