Smoothing Newton Algorithm for Linear Programming over Symmetric Cones

By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algorithm is globally convergent under suitable assumptions.

NON-INTERIOR SMOOTHING ALGORITHM FOR FRICTIONAL CONTACT PROBLEMS

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.

Smoothing Newton Algorithm for Solving Generalized Complementarity Problem

The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing Newton-type algorithm is proposed for solving the generalized complementarity problem.Under suitable assumptions, the proposed algorithm is well-defined and global convergent.

Smoothing Newton Algorithm for Nonlinear Complementarity Problem with a PFunction

By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P NCP has a nonempty solution set.This assumption is weaker than the ones used in most existing smoothing algorithms.In particular,the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P NCP without any additional assumption.

Solving frictional contact problems by two aggregate-function-based algorithms

Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.

FURTHER STUDY ON A DUAL ALGORITHM

The dual algorithm for minimax problems is further studied in this paper.The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with changing parameter in the dual algorithm is proportional to the reciprocal of the parameter,which is very important for the efficiency of the dual algorithm.At last,the numerical experiments are reported to validate the analysis results.

Convergence of a smoothing algorithm for symmetric cone complementarity problems with a nonmonotone line search

In this paper, we propose a smoothing algorithm for solving the monotone symmetric cone complementarity problems (SCCP for short) with a nonmonotone line search. We show that the nonmonotone algorithm is globally convergent under an assumption that the solution set of the problem concerned is nonempty. Such an assumption is weaker than those given in most existing algorithms for solving optimization problems over symmetric cones. We also prove that the solution obtained by the algorithm is a maximally complementary solution to the monotone SCCP under some assumptions.

EXTENSION OF SMOOTHING NEWTON ALGORITHMS TO SOLVE LINEAR PROGRAMMING OVER SYMMETRIC CONES

There recently has been much interest in studying some optimization problems over symmetric cones. This paper deals with linear programming over symmetric cones （SCLP）. The objective here is to extend the Qi-Sun-Zhou＇s smoothing Newton algorithm to solve SCLP, where characterization of symmetric cones using Jordan algebras forms the fundamental basis for our analysis. By using the theory of Euclidean Jordan algebras, the authors show that the algorithm is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical results for solving the second-order cone programming are also reported.

Dual smoothing ionospheric gradient monitoring algorithm for dual-frequency BDS GBAS

In this study,a Dual Smoothing Ionospheric Gradient Monitor Algorithm(DSIGMA)was developed for Code-Carrier Divergence(CCD)faults of dual-frequency Ground-Based Augmentation Systems(GBAS)based on the Bei Dou Navigation Satellite System(BDS).Divergence-Free(DF)combinations of the signals were used to form test statistics for a dualfrequency DSIGMA.First,the single-frequency DSIGMA was reviewed,which supports the GBAS approach service type D(GAST-D)for protection against the effect of large ionospheric gradients.The single-frequency DSIGMA was used to create a novel input scheme for the dual-frequency DSIGMA by introducing DF combinations.The steady states of the test statistics were also analysed.The monitors were characterized using BDS measurement data,whereby standard deviations of 0.0432 and 0.0639 m for the proposed two test statistics were used to calculate the monitor threshold.An extensive simulation was designed to assess the monitor performance by comparing the Probability of Missed Detection(PMD)according to the differential error with the range domain PMD limits under different fault modes.The results showed that the proposed algorithm has a higher integrity performance than the single-frequency monitor.The minimum detectable divergence with the same missed probability is less than 50%that of GAST-D.

Wireless distributed computing for cyclostationary feature detection

Recently, wireless distributed computing （WDC） concept has emerged promising manifolds improvements to current wireless technotogies. Despite the various expected benefits of this concept, significant drawbacks were addressed in the open literature. One of WDC key challenges is the impact of wireless channel quality on the load of distributed computations. Therefore, this research investigates the wireless channel impact on WDC performance when the tatter is applied to spectrum sensing in cognitive radio （CR） technology. However, a trade- off is found between accuracy and computational complexity in spectrum sensing approaches. Increasing these approaches accuracy is accompanied by an increase in computational complexity. This results in greater power consumption and processing time. A novel WDC scheme for cyclostationary feature detection spectrum sensing approach is proposed in this paper and thoroughly investigated. The benefits of the proposed scheme are firstly presented. Then, the impact of the wireless channel of the proposed scheme is addressed considering two scenarios. In the first scenario, workload matrices are distributed over the wireless channel

Optimized Design for the Plow of a Submarine Plowing Trencher

The plow of the submarine plowing trencher is one of the main functional mechanisms, and its optimization is very important. The design parameters play a very significant role in determining the requirements of the towing force of a vessel. A multi-objective genetic algorithm based on analytical models of the plow surface has been examined and applied in efforts to obtain optimal design of the plow. For a specific soil condition, the draft force and moldboard surface area which are the key parameters in the working process of the plow are optimized by finding the corresponding optimal values of the plow blade penetration angle and two surface angles of the main cutting blade of the plow. Parameters such as the moldboard side angle of deviation, moldboard lift angle, angular variation of the tangent line, and the spanning length are also analyzed with respect to the force of the moldboard surface along soil flow direction. Results show that the optimized plow has an improved plow performance. The draft forces of the main cutting blade and the moldboard are 10.6% and 7%, respectively, less than the original design. The standard deviation of Gaussian curvature of moldboard is lowered by 64.5%, which implies that the smoothness of the optimized moldboard surface is much greater than the original.

Variable structure multiple model fixed-interval smoothing

This paper focuses on fixed-interval smoothing for stochastic hybrid systems.When the truth-mode mismatch is encountered,existing smoothing methods based on fixed structure of model-set have significant performance degradation and are inapplicable.We develop a fixedinterval smoothing method based on forward-and backward-filtering in the Variable Structure Multiple Model(VSMM)framework in this paper.We propose to use the Simplified Equivalent model Interacting Multiple Model(SEIMM)in the forward and the backward filters to handle the difficulty of different mode-sets used in both filters,and design a re-filtering procedure in the model-switching stage to enhance the estimation performance.To improve the computational efficiency,we make the basic model-set adaptive by the Likely-Model Set(LMS)algorithm.It turns out that the smoothing performance is further improved by the LMS due to less competition among models.Simulation results are provided to demonstrate the better performance and the computational efficiency of our proposed smoothing algorithms.

A Homogeneous Smoothing-type Algorithm for Symmetric Cone Linear Programs

In this paper, we investigate a smoothing-type algorithm for solving the symmetric cone linear program （（SCLP） for short） by making use of an augmented system of its optimality conditions. The algorithm only needs to solve one system of linear equations and to perform one line search at each iteration. It is proved that the algorithm is globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, the algorithm may correctly detect solvability of （SCLP）. Furthermore, if （SCLP） has a solution, then the algorithm will generate a solution of （SCLP）, and if the problem is strongly infeasible, the algorithm will correctly detect infeasibility of （SCLP）.

An Improved Unsupervised Approach to Word Segmentation

ESA is an unsupervised approach to word segmentation previously proposed by Wang, which is an iterative process consisting of three phases: Evaluation, Selection and Adjustment. In this article, we propose Ex ESA, the extension of ESA. In Ex ESA, the original approach is extended to a 2-pass process and the ratio of different word lengths is introduced as the third type of information combined with cohesion and separation. A maximum strategy is adopted to determine the best segmentation of a character sequence in the phrase of Selection. Besides, in Adjustment, Ex ESA re-evaluates separation information and individual information to overcome the overestimation frequencies. Additionally, a smoothing algorithm is applied to alleviate sparseness. The experiment results show that Ex ESA can further improve the performance and is time-saving by properly utilizing more information from un-annotated corpora. Moreover, the parameters of Ex ESA can be predicted by a set of empirical formulae or combined with the minimum description length principle.

Multi-UAV Route Re-Generation Method Based on Trajectory Data

A large quantity of unmanned aerial vehicle(UAV)trajectory data related to air traffic information has important value in engineering fields.However,the cost of data and trajectory processing limits the applications,and as the number of UAVs increases rapidly,future UAVs'path data will be very large.Therefore,this paper designs a multi-UAV route re-generation method based on trajectory data,which can realize the UAVs'path data compression,de-aggregation,and regeneration tasks.Based on the trajectory data,the three-dimensional Douglas-Peucker algorithm is used to compress the trajectory data to reduce the storage space.The improved B-spline path smoothing algorithm based on the reversing control point is used to depolymerize and smooth the path.Simulation experiments show that the above multi-UAV route re-generation algorithm can obtain a more optimized path while maintaining the important characteristics of the original path.