Modified Augmented Lagrange Multiplier Methods for Large-Scale Chemical Process Optimization

Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.

Accelerated Matrix Recovery via Random Projection Based on Inexact Augmented Lagrange Multiplier Method

In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.

An optimization method for passive muzzle arc control devices in augmented railguns

In this paper,a passive muzzle arc control device(PMACD)of the augmented railguns is studied.By discussing its performance at different numbers of extra rails,a parameter optimization model is proposed.Through the calculation model,it is found that the PMACD works well in the simple railgun,which refers to the gun that there is only one pair of rails in the inner bore.The PMACD may decrease the simple railgun’s armature peak current and muzzle arc,but affect its muzzle velocity not much.However,in the augmented railguns it has different characteristics.If the parameters of the PMACD are not selected suitable.It may increase the armature peak current and muzzle arc,but greatly decrease the velocity.The reason for this problem is that the extra rails generate a strong magnetic field in front of the armature,which induces a large current to change the armature current.It is also found that when the resistance and inductance parameters of the PMACD satisfy with the optimization formula,the PMACD can also play a good role in arc suppression in the augmented railguns.Experiments of an augmented railgun with a stainless steel PMACD are carried out to verify this optimization method.Results show that the muzzle arc is obviously controlled.This work may provide a reference for the design of the muzzle arc control device.

CONTACT MODEL BASED ON AUGMENTED LAGRANGE METHOD AND ITS ENGINEERING APPLICATION

A kind of improved contact frictional model on basis of traditional Coulomb Friction model is adopted. Corresponding contact element is also given. The contact algorithm on basis of augmented Lagrange method is introduced and successfully applied to complex contact friction problem. Test example and actual engineering case all show that the algorithm of the model is efficient and computation results agree well with general rules.

An Augmented Lagrangian based Semismooth Newton Method for a Class of Bilinear Programming Problems

This paper proposes a semismooth Newton method for a class of bilinear programming problems(BLPs)based on the augmented Lagrangian,in which the BLPs are reformulated as a system of nonlinear equations with original variables and Lagrange multipliers.Without strict complementarity,the convergence of the method is studied by means of theories of semismooth analysis under the linear independence constraint qualification and strong second order sufficient condition.At last,numerical results are reported to show the performance of the proposed method.

Modified iterative method for augmented system

The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like （Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel ＆ Scientific Computations, 7（4）, 453-462 （1999）） and the modified sym- metric SOR-like （MSSOR-like） methods （Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational and Applied Mathematics, 228（4）, 424-433 （2009））.

Reduced projection augmented Lagrange bi-conjugate gradient method for contact and impact problems

Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formulation of non-linear program- ming. For contact-impact problems, a larger time-step can be adopted arriving at numer- ical convergence compared with penalty method. By establishment of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to im- prove precision and efficiency of numerical solutions. A numerical example shows that the algorithm we suggested is valid and exact.

An Augmented IB Method&Analysis for Elliptic BVP on Irregular Domains

The immersed boundary method is well-known,popular,and has had vast areas of applications due to its simplicity and robustness even though it is only first order accurate near the interface.In this paper,an immersed boundary-augmented method has been developed for linear elliptic boundary value problems on arbitrary domains(exterior or interior)with a Dirichlet boundary condition.The new method inherits the simplicity,robustness,and first order convergence of the IB method but also provides asymptotic first order convergence of partial derivatives.Numerical examples are provided to confirm the analysis.

Augmented Lagrangian Methods for Numerical Solutions to Higher Order Differential Equations

A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding numerical solutions to engineering problems. These engineering problems are described by differential equations with boundary values and are formulated as optimization of some functionals. The algorithm achieves its simplicity and versatility by choosing linear equality relations recursively for the augmented Lagrangian associated with an optimization problem. We demonstrate the formulation of an optimization functional for a 4th order nonlinear differential equation with boundary values. We also derive the associated augmented Lagrangian for this 4th order differential equation. Numerical test results are included that match up with well-established experimental outcomes. These numerical results indicate that the new algorithm is fully capable of producing accurate and stable solutions to differential equations.

An Optimization Model for the Strip-packing Problem and Its Augmented Lagrangian Method

This paper formulates a two-dimensional strip packing problem as a non- linear programming （NLP） problem and establishes the first-order optimality conditions for the NLP problem. A numerical algorithm for solving this NLP problem is given to find exact solutions to strip-packing problems involving up to 10 items. Approximate solutions can be found for big-sized problems by decomposing the set of items into small-sized blocks of which each block adopts the proposed numerical algorithm. Numerical results show that the approximate solutions to big-sized problems obtained by this method are superior to those by NFDH, FFDH and BFDH approaches.

A New Algorithm for Reducing Dimensionality of L1-CSVM Use Augmented Lagrange Method

Principal component analysis and generalized low rank approximation of matrices are two different dimensionality reduction methods. Two different dimensionality reduction algorithms are applied to the L1-CSVM model based on augmented Lagrange method to explore the variation of running time and accuracy of the model in dimensionality reduction space. The results show that the improved algorithm can greatly reduce the running time and improve the accuracy of the algorithm.

Augmented Lagrange方法在钢丝绳捻制成形摩擦接触数值模拟中的应用

钢丝绳中金属线间接触摩擦会影响捻制成形加工应力和结构强度。在经典的Coulom摩擦理论的基础上,本文采用AugmentedLagrange方法计算钢丝绳捻制过程中的法向接触力和摩擦接触力,并应用radial return径向回映法修正摩擦接触力试算值。以钢丝绳一次捻制成形过程为例,分析并讨论了摩擦系数和自扭转系数对接触应力和加工应力应变的影响,为钢丝绳成形工艺和结构强度的合理设计提供依据。

MULTILEVEL AUGMENTATION METHODS FOR SOLVING OPERATOR EQUATIONS

We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting scheme. We establish a general setting for the analysis of these methods, showing that the methods yield approximate solutions of the same convergence order as the best approximation from the subspace. These augmentation methods allow us to develop fast, accurate and stable nonconventional numerical algorithms for solving operator equations. In particular, for second kind equations, special splitting techniques are proposed to develop such algorithms. These algorithms are then applied to solve the linear systems resulting from matrix compression schemes using wavelet-like functions for solving Fredholm integral equations of the second kind. For this special case, a complete analysis for computational complexity and convergence order is presented. Numerical examples are included to demonstrate the efficiency and accuracy of the methods. In these examples we use the proposed augmentation method to solve large scale linear systems resulting from the recently developed wavelet Galerkin methods and fast collocation methods applied to integral equations of the secondkind. Our numerical results confirm that this augmentation method is particularly efficient for solving large scale linear systems induced from wavelet compression schemes.

On ε-Constraint Based Methods for the Generation of Pareto Frontiers

Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem definition. The most commonly applied methods are the normal constraint method and the normal boundary intersection method. The former suffers from the deficiency of an uneven Pareto set distribution in the case of vertical （or horizontal） sections in the Pareto frontier, whereas the latter suffers from a sparsely populated Pareto frontier when the optimization problem is numerically demanding （ill-conditioned）. The method proposed in this paper, coupled with a simple Pareto filter, addresses these two deficiencies to generate a uniform, globally optimal, well-populated Pareto frontier for any feasible bi-objective optimization problem. A number of examples are provided to demonstrate the performance of the algorithm.

The Rate of Convergence of Augmented Lagrangian Method for Minimax Optimization Problems with Equality Constraints

The augmented Lagrangian function and the corresponding augmented Lagrangian method are constructed for solving a class of minimax optimization problems with equality constraints.We prove that,under the linear independence constraint qualification and the second-order sufficiency optimality condition for the lower level problem and the second-order sufficiency optimality condition for the minimax problem,for a given multiplier vectorμ,the rate of convergence of the augmented Lagrangian method is linear with respect to||μu-μ^(*)||and the ratio constant is proportional to 1/c when the ratio|μ-μ^(*)||/c is small enough,where c is the penalty parameter that exceeds a threshold c_(*)>O andμ^(*)is the multiplier corresponding to a local minimizer.Moreover,we prove that the sequence of multiplier vectors generated by the augmented Lagrangian method has at least Q-linear convergence if the sequence of penalty parameters(ck)is bounded and the convergence rate is superlinear if(ck)is increasing to infinity.Finally,we use a direct way to establish the rate of convergence of the augmented Lagrangian method for the minimax problem with a quadratic objective function and linear equality constraints.

Fault Diagnosis Method Based on Xgboost and LR Fusion Model under Data Imbalance

Diagnosis methods based on machine learning and deep learning are widely used in the field of motor fault diagnosis.However,due to the fact that the data imbalance caused by the high cost of obtaining fault data will lead to insufficient generalization performance of the diagnosis method.In response to this problem,a motor fault monitoring system is proposed,which includes a fault diagnosis method(Xgb_LR)based on the optimized gradient boosting decision tree(Xgboost)and logistic regression(LR)fusion model and a data augmentation method named data simulation neighborhood interpolation(DSNI).The Xgb_LR method combines the advantages of the two models and has positive adaptability to imbalanced data.Simultaneously,the DSNI method can be used as an auxiliary method of the diagnosis method to reduce the impact of data imbalance by expanding the original data(signal).Simulation experiments verify the effectiveness of the proposed methods.

Optimization of multibody systems based on the generalized-α projection method for DAEs

Efficient optimization strategy of multibody systems is developed in this paper. Aug- mented Lagrange method is used to transform constrained optimal problem into unconstrained form firstly. Then methods based on second order sensitivity are used to solve the unconstrained problem, where the sensitivity is solved by hybrid method. Generalized-α method and generalized-α projection method for the differential-algebraic equation, which shows more efficient properties with the lager time step, are presented to get state variables and adjoint variables during the optimization procedure. Numerical results validate the accuracy and efficiency of the methods is presented.

大吨位转体桥梁不平衡力矩计算方法优化研究

针对常用的不平衡力矩计算方法无法适应于大吨位转体桥梁而造成较大计算误差的问题,基于常用的球铰转动法和球铰应力差法,以某大吨位转体桥为背景,对2种方法的不平衡力矩计算结果进行对比,以确定适合大吨位转体桥梁不平衡力矩计算方法;建立球铰有限元模型,分析不平衡力矩对球铰应力差分布规律;采用增广拉格朗日方程对基于球铰应力差法的不平衡力矩计算公式进行优化,并以多座桥梁为例验证优化公式的适用性。结果表明:球铰应力差法与球铰转动法的不平衡力矩计算值相对误差较小;球铰两侧应力差值的大小随着与球铰中心距离的增加呈现先增大后减小的变化趋势;不平衡力矩有限元分析值大于实测值,且两者的相对误差随着不平衡力矩的增加显著增大,最大相对误差为33.4%,优化后的球铰应力差法计算得到的不平衡力矩值与实测值的相对误差在15%以内,表明优化效果良好。

夏季干旱对大气污染物的影响与驱动因素

利用2022年1月~8月中国300个地级市大气污染物(PM_(2.5),PM_(10),NO_(2)和SO_(2))小时浓度数据及同期气象数据,研究夏季干旱对大气污染物的影响及其驱动因素.研究结果显示:干旱期间和正常期间长株潭城市群PM_(2.5),PM_(10),NO_(2)和SO_(2)浓度累积分布存在显著差异,且3个城市间同类污染物浓度的累积分布模式具有明显一致性.夏季干旱事件对PM_(2.5),PM_(10),NO_(2)和SO_(2)污染具有一定的抑制作用,其NO_(2)分别累积降低45.27μg/m^(3)(长沙),48.53μg/m^(3)(株洲)和13.40μg/m^(3)(湘潭);PM_(10)累积降低了56.30μg/m^(3)(长沙),55.68μg/m^(3)(株洲)和23.73μg/m^(3)(湘潭);PM_(2.5)分别累积降低了36.54μg/m^(3)(长沙),24.48μg/m^(3)(株洲)和37.52μg/m^(3)(湘潭);SO_(2)分别累积降低了2.19μg/m^(3)(长沙),18.51μg/m^(3)(株洲)和4.35μg/m^(3)(湘潭).干旱通过气温,气压,风速和相对湿度4个驱动因素来降低PM_(2.5),PM_(10),NO_(2)和SO_(2)浓度.

激活后增强训练法在田径运动中的应用与效果研究

为了更加有效地提高体育专业学生的运动成绩,优化田径运动训练方法,引入了激活后增强训练法,通过实验与常规抗阻训练的训练效果进行对比。实验结果表明,激活后增强训练法能够更有效地增强爆发力,提高体育项目成绩。激活后增强训练法在研究中的平均提升幅度达到了8.68%,在相同的测试项目中,相较于传统抗阻训练法的提升幅度提高了4.58%。激活后增强训练法不仅结合了抗阻训练的优点,同时引入了神经-肌肉的“激活”概念,能够为体育训练方法的改革提供理论和数据支持。