In this paper, we present new stochastic methods for solving two important classes of nonconvex optimization problems. We first introduce a randomized accelerated proximal gradient (RapGrad) method for solving a class of nonconvex optimization problems whose objective function consists of the summation of m components, and show that it can significantly reduce the number of gradient computations especially when the condition number L/µ (i.e., the ratio between the Lipschitz constant and negative curvature) is large. More specifically, RapGrad can save up to O( √ m) gradient computations than existing batch nonconvex accelerated gradient methods. Moreover, the number of gradient computations required by RapGrad can be O(m

Luteolin is a falconoid compound, which exhibits anticancer properties, however, its contribution to Sirt1-mediated apoptosis in human non-small cell lung cancer remains to be elucidated. The present study confirmed that the anticancer effect of luteolin on NCI-H460 cells was through Sirt1-mediated apoptosis. The NCI-H460 cells were treated with different concentrations of luteolin, and a 3-(4,5-dimeth yl-2-thiazolyl)-2,5-diphnyl-2H-tetrazolium bromide assay, cell cycle analysis and annexin-V/fluorescein isothiocyanate and propidium double staining were performed to assess the apoptotic effect of luteolin. Wound healing and Transwell assays were performed to confirm the inhibition of NCI-H460 cell migration. The protein levels of Sirt1 were knocked down in the NCI-H460 cells using a lentivirus to further investigate the role of this protein, and the expression levels of the apoptotic associated proteins, Bad, Bcl-2, Bax, caspase-3 and Sirt1, were measured using western blotting. The results of the present study demonstrated that luteolin exerted an anticancer effect against NCI-H460 cells through Sirt1-mediated apoptosis and the inhibition of cell migration.

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We consider the capacitated multitrip vehicle routing problem with time windows (CMTVRPTW), where vehicles are allowed to make multiple trips. The ability to perform multiple trips is necessary for some real-world applications where the vehicle capacity, the trip duration, or the number of drivers or vehicles is limited. However, it substantially increases the solution difficulty in view of the additional trip scheduling aspect. We propose an exact price-cut-and-enumerate method (EPCEM) that solves a novel superstructure-based formulation inspired by Paradiso et al. ( 2020 ). The EPCEM obtains a tight lower bound by an alternating column and row generation method and computes a valid upper bound in the early stage of the algorithm. It obtains an optimal solution and further proves its optimality by a new multiphase sift-and-cut method. Computationally, the EPCEM significantly outperforms the state-of-the-art exact method that only proves optimality for 9 of the 27 test instances with 50 customers. In particular, the EPCEM solves all test instances with up to 70 customers to optimality for the first time and obtains near-optimal solutions with an average optimality gap of no more than 0.3% for instances with 80 to 100 customers. From a practical point of view, solving the CMTVRPTW by the EPCEM yields a solution that, on average, uses at least 45% fewer vehicles and increases the travel cost by no more than 7% compared with the solution to the standard CVRPTW.

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The doubly fed induction generator (DFIG) is investigated. Its mathematical model under d-q axis is deduced. According to 2MW mainstream DFIG actual parameters the chaotic behaviors are demonstrated to appear in a certain range of parameter values or under certain working conditions. Based on active control method, an active sliding mode controller is designed, which enables chaotic systems to be stablized under arbitrary initial conditions. The stability of the controlling method is analyzed by Lyapunov stability theorem. Finally, numerical results are presented for the DFIG system. This method may realize the chaos synchronization, and both the stability and the robustness are good.

This paper presents a novel six-degree-of-freedom (6-DOF) parallel platform that is used as the third mirror adjustment system of a large space telescope. In order to meet the design requirements of high precision, a large load–size ratio, and high stiffness in both the transverse and the vertical directions, the parallel platform is designed to be a 6-P-RR-R-RR structure via use of offset RR-joints. The inverse kinematics problem of the designed platform with offset RR-joints is much more complicated than that of a parallel platform with common universal joints owing to the presence of joint-dependent variables in the former problem. In this study, inverse kinematics of the designed parallel platform is mathematically modeled and the Newton–Raphson numerical iterative computation is performed. The accuracy and effectiveness of the proposed mathematical approach are verified by numerical co-simulations using MATLAB and ADAMS. The initial position of the platform is determined by a precision measuring arm. A test system is constructed, and then inverse kinematics solution, resolutions and adjusting steps accuracies of the platform are tested using grating length gauges. Motion strokes of the parallel mechanism are measured using laser tracker.

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