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As an extension of linear complementary problem, tensor complementary problem has been effectively applied in n-person noncooperative game. And a multitude of researchers have focused on its properties and theories, while the valid algorithms for tensor complementary problem is still deficient. In this paper, stimulated by the potential reduction method for linear complementarity problem, we present a new algorithm for the tensor complementarity problem, which combines the idea of damped Newton method and the interior point method. Utilizing the new algorithm, we settle the tensor complementary problem with the underlying tensor being diagonalizable and positive definite. Furthermore, the global convergence of the iterative scheme is theoretically guaranteed and the given preliminary numerical experiments indicate the efficiency of the method.

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In the fields of wireless communication and data processing, there are varieties of mathematical optimization problems, especially nonconvex and nonsmooth problems.For these problems, one of the biggest difficulties is how to improve the speed of solution. To this end, here we mainly focused on a minimization optimization model that is nonconvex and nonsmooth. Firstly, an inertial Douglas-Rachford splitting (IDRS) algorithm was established, which incorporate the inertial technology into the framework of the Douglas-Rachford splitting algorithm. Then, we illustrated the iteration sequence generated by the proposed IDRS algorithm converges to a stationary point of the nonconvex nonsmooth optimization problem with the aid of the Kurdyka-Łojasiewicz property. Finally, a series of numerical experiments were carried out to prove the effectiveness of our proposed algorithm from the perspective of signal recovery. The results are implicit that the proposed IDRS algorithm outperforms another algorithm.

An understanding of the walking patterns of groups of pedestrians in an evacuation is critical for the establishment of policies, procedures, and organizational structures to respond effectively to emergencies. Groups of pedestrians compose a crowd in which pedestrian motions are significantly constrained to maintain cohesion. On the basis of behavior theory, this paper proposes a multiagent model for the simulation of crowds of pedestrians. The main innovative aspect of this model is the genuine representation of the patterns of movement of groups of pedestrians. Patterns of movement consisting of the line-abreast pattern, the chain pattern, and the mixed pattern were investigated, and their influences on evacuations were evaluated quantitatively by taking into account the discrepant densities, disparate distributions of the proportions of pedestrian groups of different sizes, and heterogeneous velocities of groups of pedestrians. The simulation results show that the walking patterns of groups of pedestrians have a significant influence on the dynamics of pedestrian evacuation. The chain pattern was safer when the time of evacuation under high-density conditions was considered, and the mixed pattern had a better performance under moderate-density conditions. Moreover, the influence of patterns of movement was distinct with different distributions of pedestrian groups of different sizes; the chain pattern had the highest evacuation efficiency among the three patterns of pedestrian movement. In addition, a homogeneous velocity condition had a higher evacuation efficiency than a heterogeneous velocity condition. Thus, a chain pattern with a homogeneous velocity is recommended as the optimal pattern of movement in pedestrian evacuations when the safety and efficiency of plans and designs for the evacuation of pedestrian traffic with the different patterns of movement are considered.