Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.

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.

A SUPERLINEARLY CONVERGENT SPLITTING FEASIBLE SEQUENTIAL QUADRATIC OPTIMIZATION METHOD FOR TWO-BLOCK LARGE-SCALE SMOOTH OPTIMIZATION

This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.

A Smooth Bidirectional Evolutionary Structural Optimization of Vibrational Structures for Natural Frequency and Dynamic Compliance

A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load.A weighted function is introduced to regulate the mass and stiffness matrix of an element,which has the inefficient element gradually removed from the design domain as if it were undergoing damage.Aiming at maximizing the natural frequency of a structure,the frequency optimization formulation is proposed using the SBESO technique.The effects of various weight functions including constant,linear and sine functions on structural optimization are compared.With the equivalent static load(ESL)method,the dynamic stiffness optimization of a structure is formulated by the SBESO technique.Numerical examples show that compared with the classic BESO method,the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function.It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.

Aerodynamic design on high-speed trains

Compared with the traditional train,the operational speed of the high-speed train has largely improved,and thedynamicenvironmentofthetrainhaschangedfromoneof mechanical domination to one of aerodynamic domination.The aerodynamic problem has become the key technological challenge of high-speed trains and significantl affects the economy,environment,safety,and comfort.In this paper,the relationships among the aerodynamic design principle,aerodynamic performance indexes,and design variables are firs studied,and the research methods of train aerodynamics are proposed,including numerical simulation,a reducedscale test,and a full-scale test.Technological schemes of train aerodynamics involve the optimization design of the streamlined head and the smooth design of the body surface.Optimization design of the streamlined head includes conception design,project design,numerical simulation,and a reduced-scale test.Smooth design of the body surface is mainly used for the key parts,such as electric-current collecting system,wheel truck compartment,and windshield.The aerodynamic design method established in this paper has been successfully applied to various high-speed trains（CRH380A,CRH380 AM,CRH6,CRH2 G,and the Standard electric multiple unit（EMU）） that have met expected design objectives.The research results can provide an effective guideline for the aerodynamic design of high-speed trains.

OPTIMAL TORQUE CONTROL STRATEGY FOR PARALLEL HYBRID ELECTRIC VEHICLE WITH AUTOMATIC MECHANICAL TRANSMISSION

In parallel hybrid electrical vehicle （PHEV） equipped with automatic mechanical transmission （AMT）, the driving smoothness and the clutch abrasion are the primary considerations for powertrain control during gearshift and clutch operation. To improve these performance indexes of PHEV, a coordinated control system is proposed through the analyzing of HEV powertrain dynamic characteristics. Using the method of minimum principle, the input torque of transmission is optimized to improve the driving smoothness of vehicle. Using the methods of fuzzy logic and fuzzy-PID, the engaging speed of clutch and the throttle opening of engine are manipulated to ensure the smoothness of clutch engagement and reduce the abrasion of clutch friction plates. The motor provides the difference between the required input torque of transmission and the torque transmitted through clutch plates. Results of simulation and experiments show that the proposed control strategy performs better than the contrastive control system, the smoothness of driving and the abrasion of clutch can be improved simultaneously.

OPTIMAL SMOOTHING FOR MICROPHONE ARRAY POST-FILTERING UNDER A COMBINED DETERMINISTIC-STOCHASTIC HYBRID MODEL

This paper shows the importance of the optimal smoothing scheme in Microphone Array Post-Filtering(MAPF) under a combined Deterministic-Stochastic Hybrid Model(DSHM).We reveal that some of the well-known MAPF algorithms may cause serious speech distortion without using the optimal smoothing scheme,which is resulted from oversmoothing the raw periodogram over time.Using a minimum conditional mean square error criterion,we derive the optimal smoothing factor under the DSHM,where the Deterministic-to-Stochastic-Ratio(DSR) and the stationarity determine the value of the optimal smoothing factor.The optimal smoothing scheme is applied to the Tran-sient-Beam-to-Reference-Ratio(TBRR)-based MAPF algorithm and experimental results show its better performance in terms of both the Log-Spectral Distance(LSD) and the Perceptual Evaluation of Speech Quality(PESQ).

New smooth gap function for box constrained variational inequalities

A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

An Efficient Approach to a Class of Non-smooth Optimization Problems

This paper presents an entropy-based smoothing technique for solving a class of non-smooth optimization problems that are in some way related to the maximum function.Basic ideas concerning this approach are that we replace the non-smooth maximum function by a smooth one,called aggregate function,which is derived by employing the maximum entropy principle and its useful properties are proved.Wilh this smoothing technique,both unconstrained and constrained mimma.x problems are transformed into unconstrained optimization problems of smooth functions such that this class of non-smooth optimization problems can be solved by some existing unconstrained optimization softwares for smooth functions The present approach can be very easily implemented on computers with very fast and-.Inhie convergence.