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This paper introduces a bilevel programming model for optimizing transit network departure frequency. In the upper-level model, user satisfaction is reflected by considering congestion effects in the cost function. The lower-level assignment model simulates passenger travel behavior more realistically by incorporating congestion effects. This problem is solved by a heuristic gradient descent algorithm, where an approximation of the gradient is obtained at each iteration by using sensitivity analysis for transit equilibrium problems. The effectiveness of the proposed model and algorithm is demonstrated through two test examples, one of which involves a real-world scenario comprising over 130 transit lines. Numerical results conclusively indicate that the incorporation of congestion effects in the proposed model leads to improved transit system performance and enhanced user satisfaction. [ABSTRACT FROM AUTHOR]

The proportionate affine projection sign subband adaptive filter (PAP-SSAF) has a better performance than the affine projection sign subband adaptive filter (AP-SSAF) when we eliminate the echoes. Still, the robustness of the PAP-SSAF algorithm is insufficient under unknown environmental conditions. Besides, the best balance remains to be found between low steady-state misalignment and fast convergence rate. In order to solve this problem, we propose a normalized combination of PAP-SSAF (NCPAP-SSAF) based on the normalized adaption schema. In this paper, a power normalization adaptive rule for mixing parameters is proposed to further improve the performance of the NCPAP-SSAF algorithm. By using Nesterov's accelerated gradient (NAG) method, the mixing parameter of the control combination can be obtained with less time consumed when we take the l1-norm of the subband error as the cost function. We also test the algorithmic complexity and memory requirements to illustrate the rationality of our method. In brief, our study contributes a novel adaptive filter algorithm, accelerating the convergence speed, reducing the steady-state error, and improving the robustness. Thus, the proposed method can be utilized to improve the performance of echo cancellation. We will optimize the combination structure and simplify unnecessary calculations to reduce the algorithm's computational complexity in future research. [ABSTRACT FROM AUTHOR]

In this paper, we consider stochastic vector variational inequality problems (SVVIPs). Because of the existence of stochastic variable, the SVVIP may have no solutions generally. For solving this problem, we employ the regularized gap function of SVVIP to the loss function and then give a low-risk conditional value-at-risk (CVaR) model. However, this low-risk CVaR model is difficult to solve by the general constraint optimization algorithm. This is because the objective function is nonsmoothing function, and the objective function contains expectation, which is not easy to be computed. By using the sample average approximation technique and smoothing function, we present the corresponding approximation problems of the low-risk CVaR model to deal with these two difficulties related to the low-risk CVaR model. In addition, for the given approximation problems, we prove the convergence results of global optimal solutions and the convergence results of stationary points, respectively. Finally, a numerical experiment is given. [ABSTRACT FROM AUTHOR]

Aiming at the problem that stereo matching accuracy is easily affected by noise and amplitude distortion, a stereo matching algorithm based on HSV color space and improved census transform is proposed. In the cost calculation stage, the color image is first converted from RGB space to HSV space; moreover, the hue channel is used as the matching primitive to establish the hue absolute difference (HAD) cost calculation function, which reduces the amount of calculation and enhances the robustness of matching. Then, to solve the problem of the traditional census transform overrelying on the central pixel and to improve the noise resistance of the algorithm, an improved census method based on neighborhood weighting is also proposed. Finally, the HAD cost and the improved census cost are nonlinearly fused as the initial cost. In the aggregation stage, an outlier elimination method based on confidence interval is proposed. By calculating the confidence interval of the aggregation window, this paper eliminates the cost value that is not in the confidence interval and subsequently filters as well as aggregates the remaining costs to further reduce the noise interference and improve the matching accuracy. Experiments show that the proposed method can not only effectively suppress the influence of noise, but also achieve a more robust matching effect in scenes with changing exposure and lighting conditions. [ABSTRACT FROM AUTHOR]

This paper studies the discrete-time stochastic linear quadratic (LQ) problem with a second moment constraint on the terminal state, where the weighting matrices in the cost functional are allowed to be indefinite. By means of the matrix Lagrange theorem, a new class of generalized difference Riccati equations (GDREs) is introduced. It is shown that the well-posedness, and the attainability of the LQ problem and the solvability of the GDREs are equivalent to each other. [ABSTRACT FROM AUTHOR]

The constant parameter identification problem in the Kirchhoff-type equation with viscosity is studied. The problem is formulated by a minimization of quadratic cost functionals by distributive measurements. The existence of optimal parameters and necessary optimality conditions for the parameters are proved [ABSTRACT FROM AUTHOR]