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This paper considers the regularization continuation method and the trust-region updating strategy for the optimization problem with linear equality constraints.The proposed method utilizes the linear conservation law of the regularization continuation method such that it does not need to compute the correction step for preserving the feasibility other than the previous continuation methods and the quasi-Newton updating formulas for the linearly constrained optimization problem. Moreover, the new method uses the special limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) formula as the preconditioning technique to improve its computational efficiency in the well-posed phase, and it uses the inverse of the regularized two-sided projection of the Lagrangian Hessian as the pre-conditioner to improve its robustness. Numerical results also show that the new method is more robust and faster than the traditional optimization method such as the alternating direction method of multipliers (ADMM),the sequential quadratic programming (SQP) method (the built-in subroutine fmincon.m of the MATLAB2020a environment), and the recent continuation method (Ptctr). The computational time of the new method is about 1/3 of that of SQP (fmincon.m). Finally, the global convergence analysis of the new method is also given., Comment: arXiv admin note: substantial text overlap with arXiv:2101.07055, arXiv:2012.14808

The global minimum point of an optimization problem is of interest in engineering fields and it is difficult to be solved, especially for a nonconvex large-scale optimization problem. In this article, we consider a new memetic algorithm for this problem. That is to say, we use the continuation Newton method with the deflation technique to find multiple stationary points of the objective function and use those found stationary points as the initial seeds of the evolutionary algorithm, other than the random initial seeds of the known evolutionary algorithms. Meanwhile, in order to retain the usability of the derivative-free method and the fast convergence of the gradient-based method, we use the automatic differentiation technique to compute the gradient and replace the Hessian matrix with its finite difference approximation. Accordingto our numerical experiments, this new algorithm works well for unconstrained optimization problems and finds their global minima efficiently, in comparison to the other representative global optimization methods such as the multi-start methods (the built-in subroutine GlobalSearch.m of MATLAB R2021b, GLODS and VRBBO), the branch-and-bound method (Couenne, a state-of-the-art open-source solver for mixed integer nonlinear programming problems), and the derivative-free algorithms (CMA-ES and MCS). Mathematics Subject Classification (2010) 65K05 · 65L05 · 65L20

A straightforward aerobic oxidative esterification of aryl aldehydes with alcohols has been developed for the synthesis of substituted esters by employing vitamin B1 as a cost-effective, metal-free, and eco-friendly NHC catalyst. Air is used as a green terminal oxidant. The reaction is a useful addition to the existing NHC-catalytic oxidative esterification.

This paper considers the generalized continuation Newton method and thetrust-region updating strategy for the underdetermined system of nonlinear equations. Moreover, in order to improve its computational efficiency, the new method will not update the Jacobian matrix when the current Jacobian matrix performs well. The numerical results show that the new method is more robust and faster than the traditional optimization method such as the Levenberg-Marquardt method (a variant of trust-region methods, the built-in subroutine fsolve.m of the MATLAB R2020a environment). The computational time of the new method is about 1/8 to 1/50 of that of fsolve. Furthermore, it also proves the global convergence and the local superlinear convergence of the new method under some standard assumptions., arXiv admin note: text overlap with arXiv:2006.02634, arXiv:2006.07568

This paper considers an explicit continuation method and the trust-region updating strategy for the unconstrained optimization problem. Moreover, in order to improve its computational efficiency and robustness, the new method uses the switching preconditioning technique. In the well-conditioned phase, the new method uses the L-BFGS method as the preconditioning technique in order to improve its computational efficiency. Otherwise, the new method uses the inverse of the Hessian matrix as the pre-conditioner in order to improve its robustness. Numerical results also show that the new method is more robust and faster than the traditional optimization method such as the trust-region method and the line search method. The computational time of the new method is about one percent of that of the trust-region method (the subroutine fminunc.m of the MATLAB2019a environment is set by the trust-region method) or one fifth of that of the line search method (fminunc.m is set by the quasi-Newton method) for the large-scale problem. Finally, the global convergence analysis of the new method is also given.

International audience; Dendritic cells (DCs) are mononuclear phagocytes that are specialized in the induction and functional polarization of effector lymphocytes, thus orchestrating immune defenses against infections and cancer. The population of DC encompasses distinct cell types that vary in their efficacy for complementary functions and are thus likely involved in defending the body against different threats. Plasmacytoid DCs specialize in the production of high levels of the antiviral cytokines type I interferons. Type 1 conventional DCs (cDC1s) excel in the activation of cytotoxic CD8 + T cells (CTLs) which are critical for defense against cancer and infections by intracellular pathogens. Type 2 conventional DCs (cDC2s) prime helper CD4 + T cells for the production of type 2 cytokines underpinning immune defenses against worms or of IL-17 promoting control of infections by extracellular bacteria or fungi. Hence, clinically manipulating the development and functions of DC types could have a major impact for improving treatments against many diseases. However, the rarity and fragility of human DC types is impeding advancement towards this goal. To overcome this roadblock, major efforts are ongoing to generate in vitro large numbers of distinct human DC types. We review here the current state of this research field, emphasizing recent breakthrough and proposing future priorities. We also pinpoint the necessity to develop a consensus nomenclature and rigorous methodologies to ensure proper identification and characterization of human DC types. Finally, we elaborate on how faithful in vitro models of human DC types can accelerate our understanding of the biology of these cells and the engineering of next generation vaccines or immunotherapies against viral infections or cancer.

For nonlinear equations, the homotopy methods (continuation methods) are popular in engineering fields since their convergence regions are large and they are quite reliable to find a solution. The disadvantage of the classical homotopy methods is that their computational time is heavy since they need to solve many auxiliary nonlinear systems during the intermediate continuation processes. In order to overcome this shortcoming, we consider the special explicit continuation Newton method with the residual trust-region time-stepping scheme for this problem. According to our numerical experiments, the new method is more robust and faster to find the required solution of the real-world problem than the traditional optimization method (the built-in subroutine fsolve.m of the MATLAB environment) and the homotopy continuation methods(HOMPACK90 and NAClab). Furthermore, we analyze the global convergence and the local superlinear convergence of the new method.

The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to solve this practical problem efficiently, this paper constructs a continuation method with the trusty time-stepping scheme for the linearly equality-constrained optimization problem at every sampling time. At every iteration, the new method only solves a system of linear equations other than the traditional optimization method such as the sequential quadratic programming (SQP) method, which needs to solve a quadratic programming subproblem. Consequently, the new method can save much more computational time than SQP. Numerical results show that the new method works well for this problem and its consumed time is about one fifth of that of SQP (the built-in subroutine fmincon.m of the MATLAB2018a environment) or that of the traditional dynamical method (the built-in subroutine ode15s.m of the MATLAB2018a environment). Furthermore, we also give the global convergence analysis of the new method.

In this paper, a method of improving vertical positioning accuracy with the global positioning system information and barometric pressure values is proposed. Firstly, we clear null values for the raw data collected in various environments, and use the 3 $$\sigma$$ -rule to identify outliers. Secondly, the weighted multinomial logistic regression (WMLR) classifier is trained to obtain the predicted altitude of outliers. Finally, in order to verify its effect, we compare the multinomial logistic regression (MLR) method, the WMLR method, and the support vector machine (SVM) method for the cleaned dataset which is regarded as the test baseline. The numerical results show that the vertical positioning accuracy is improved from 5.9 m (the MLR method), 5.4 m (the SVM method) to 5 m (the WMLR method) for 67% test points.

Problem statement: There is a large demand for wireless Location-Based Service (LBS) and it is provided by many wireless cellular systems. In process of positioning a Mobile Station (MS), the computing speed is as important as the positioning accuracy and the algorithm should also be resistant to environmental influences. Approach: A new positioning method based on Weighted Centroid Correction Localization (WCCL) for wireless cellular systems is introduced in this article. Firstly, referring to the receiving-state of an MS in cellular systems, it computes a weighted centroid of surrounding Base Stations (BSs) as a rough approximate position of the MS. Then, according to the distances between the MS and the BSs being less or bigger than the computed distances between the BSs and the weighted centroid, it corrects the coordinate of the weighted centroid towards the directions of the BSs by moving it closer or farther in turn. Results: According to our experiments, WCCL improves the positioning accuracy, as well as to provide a better resistance to environmental influences. Conclusion: As a modified centroid-based localization algorithm, WCCL obtains weighting factors from the receiving-state of MS in multi-cells structured cellular systems and obtains a better positioning result in cellular systems without updating the network equipment. Therefore, for the cellular positioning problem, WCCL algorithm can be an alternate solution.

Recently, a continuous method has been proposed by Golub and Liao as an alternative way to solve the minimum and interior eigenvalue problems. According to their numerical results, their method seems promising. This article is an extension along this line. In this article, firstly, we convert an eigenvalue problem to an equivalent constrained optimization problem. Secondly, using the Karush–Kuhn–Tucker conditions of this equivalent optimization problem, we obtain a variant of the Rayleigh quotient gradient flow, which is formulated by a system of differential-algebraic equations. Thirdly, based on the Rayleigh quotient gradient flow, we give a practical numerical method for the minimum and interior eigenvalue problems. Finally, we also give some numerical experiments of our method, the Golub and Liao method, and EIGS (a Matlab implementation for computing eigenvalues using restarted Arnoldi’s method) for some typical eigenvalue problems. Our numerical experiments indicate that our method seems promising for most test problems.

A new 3D fingerprinting positioning scheme based on cellular networks is proposed by using implicit information of the location around geographic environments. Compared with original fingerprint positioning scheme, singular measurement is processed at the beginning of the proposed scheme. The main improvement of our proposed scheme is to employ cell matching degree and choose the best reasonable fingerprint according to the correlation of its surrounding points. Additionally, in order to improve searching efficiency, a new searching window is introduced. Finally, compared with the maximum likelihood method and the weighted K nearest neighbors method, the promising numerical results are also presented.

This paper gives a new prediction-correction method based on the dynamical system of differential-algebraic equations for the smallest generalized eigenvalue problem. First, the smallest generalized eigenvalue problem is converted into an equivalent-constrained optimization problem. Second, according to the Karush-Kuhn-Tucker conditions of this special equality-constrained problem, a special continuous dynamical system of differential-algebraic equations is obtained. Third, based on the implicit Euler method and an analogous trust-region technique, a prediction-correction method is constructed to follow this system of differential-algebraic equations to compute its steady-state solution. Consequently, the smallest generalized eigenvalue of the original problem is obtained. The local superlinear convergence property for this new algorithm is also established. Finally, in comparison with other methods, some promising numerical experiments are presented.

Wireless sensor networks (WSNs) consist of a large number of low-cost miniature sensors, which can be applied to battlefield surveillance, environmental monitoring, target tracking, and other applications related to the positions of sensors. The location information of sensors is of great importance for wireless sensor networks. In this paper, we propose a new localization algorithm for the wireless sensor network based on time difference of arrival (TDOA), which is a typical algorithm in the wireless localization field. In order to improve the localization accuracy of a sensor, a new strategy is proposed for a localized sensor being upgraded to an anchor node, which is used to localize the position of the next sensor. Performance analysis and simulation results show that the revised TODA localization algorithm has the higher localization accuracy when compared with the original TDOA location method.