球约束凸二次规划的一个算法

针对球约束凸二次规划问题，利用Lagrange对偶将其转化为无约束优化问题，然后运用单纯形法对其求解，获得原问题的最优解。最后，对文中给出的算法给出了论证。     

An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimization

This paper presents an improved weighting method for multicriteria structural optimization. By introducing artificial design variables, here called as multibounds formulation (MBF), we demonstrate mathematically that the weighting combination of criteria can be transformed into a simplified problem with a linear objective function. This is a unified formulation for one criterion and multicriteria problems. Due to the uncoupling of involved criteria after the transformation, the extension and the adaptation of monotonic approximation‐based convex programming methods such as the convex linearization (CONLIN) or the method of moving asymptotes (MMA) are made possible to solve multicriteria problems as efficiently as for one criterion problems. In this work, a multicriteria optimization tool is developed by integrating the multibounds formulation with the CONLIN optimizer and the ABAQUS finite element analysis system. Some numerical examples are taken into account to show the efficiency of this approach. Copyright © 2001 John Wiley & Sons, Ltd.     

A Combined Convex Approximation—Interior Point Approach for Large Scale Nonlinear Programming

The method of moving asymptotes (MMA) and its globally convergent extension SCP (sequential convex programming) are known to work well in the context of structural optimization. The two main reasons are that the approximation scheme used for the objective function and the constraints fits very well to these applications and that at an iteration point a local optimization model is used such that additional expensive function and gradient evaluations of the original problem are avoided. The subproblems that occur in both methods are special nonlinear convex programs and have traditionally been solved using a dual approach. This is now replaced by an interior point approach. The latter one is more suitable for large problems because sparsity properties of the original problem can be preserved and the separability property of the approximation functions is exploited. The effectiveness of the new method is demonstrated by a few examples dealing with problems of structural optimization.     

A quadratic approximation for structural topology optimization

In topology optimization, it is customary to use reciprocal‐like approximations, which result in monotonically decreasing approximate objective functions. In this paper, we demonstrate that efficient quadratic approximations for topology optimization can also be derived, if the approximate Hessian terms are chosen with care. To demonstrate this, we construct a dual SAO algorithm for topology optimization based on a strictly convex, diagonal quadratic approximation to the objective function. Although the approximation is purely quadratic, it does contain essential elements of reciprocal‐like approximations: for self‐adjoint problems, our approximation is identical to the quadratic or second‐order Taylor series approximation to the exponential approximation. We present both a single‐point and a two‐point variant of the new quadratic approximation. Copyright © 2009 John Wiley & Sons, Ltd.     

A new deterministic global optimization method for general twice-differentiable constrained nonlinear programming problems

A deterministic global optimization method that is applicable to general nonlinear programming problems composed of twice-differentiable objective and constraint functions is proposed. The method hybridizes the branch-and-bound algorithm and a convex cut function (CCF). For a given subregion, the difference of a convex underestimator that does not need an iterative local optimizer to determine the lower bound of the objective function is generated. If the obtained lower bound is located in an infeasible region, then the CCF is generated for constraints to cut this region. The cutting region generated by the CCF forms a hyperellipsoid and serves as the basis of a discarding rule for the selected subregion. However, the convergence rate decreases as the number of cutting regions increases. To accelerate the convergence rate, an inclusion relation between two hyperellipsoids should be applied in order to reduce the number of cutting regions. It is shown that the two-hyperellipsoid inclusion relation is determined by maximizing a quadratic function over a sphere, which is a special case of a trust region subproblem. The proposed method is applied to twelve nonlinear programming test problems and five engineering design problems. Numerical results show that the proposed method converges in a finite calculation time and produces accurate solutions.     

A method of steepest ascent for multiresponse surface optimization using a desirability function method

Multiresponse problems are common in product or process development. A conventional approach for optimizing multiple responses is to use a response surface methodology (RSM), and this approach is called multiresponse surface optimization (MRSO). In RSM, the method of steepest ascent is widely used for searching for an optimum region where a response is improved. In MRSO, it is difficult to directly apply the method of steepest ascent because MRSO includes several responses to be considered. This paper suggests a new method of steepest ascent for MRSO, which accounts for tradeoffs between multiple responses. It provides several candidate paths of steepest ascent and allows a decision maker to select the most preferred path. This generation and selection procedure is helpful to better understand the tradeoffs between the multiple responses, and ultimately, it moves the experimental region to a good region where a satisfactory compromise solution exists. A hypothetical example is employed for illustrating the proposed procedure. The results of this case study show that the proposed method searches the region containing an optimum where a satisfactory compromise solution exists.     

The method of fundamental solutions for steady-state groundwater flow problems

The method of fundamental solutions is a meshless method. Only boundary collocation points are needed during the whole solution process. It has the merits of mathematical simplicity, ease of programming, high solution accuracy, and others. In this paper, the method of fundamental solutions is applied to simulate 2D steady-state groundwater flow problems. The principle of superposition is used during the whole solution process. Numerical results are compared with the multiquadrics method and the mixed finite element method as well as analytical solutions. It is shown that the method of fundamental solutions is promising in dealing with steady groundwater flow problems.     

Boundary element‐free method (BEFM) and its application to two‐dimensional elasticity problems

In this study, we first discuss the moving least‐square approximation (MLS) method. In some cases, the MLS may form an ill‐conditioned system of equations so that the solution cannot be correctly obtained. Hence, in this paper, we propose an improved moving least‐square approximation (IMLS) method. In the IMLS method, the orthogonal function system with a weight function is used as the basis function. The IMLS has higher computational efficiency and precision than the MLS, and will not lead to an ill‐conditioned system of equations. Combining the boundary integral equation (BIE) method and the IMLS approximation method, a direct meshless BIE method, the boundary element‐free method (BEFM), for two‐dimensional elasticity is presented. Compared to other meshless BIE methods, BEFM is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied easily; hence, it has higher computational precision. For demonstration purpose, selected numerical examples are given. Copyright © 2005 John Wiley & Sons, Ltd.     

A demonstration of the improved efficiency of the canonical coordinates method using nonlinear combined heat and power economic dispatch problems

Economic dispatch is the short-term determination of the optimal output from a number of electricity generation facilities to meet the system load while providing power. As such, it represents one of the main optimization problems in the operation of electrical power systems. This article presents techniques to substantially improve the efficiency of the canonical coordinates method (CCM) algorithm when applied to nonlinear combined heat and power economic dispatch (CHPED) problems. The improvement is to eliminate the need to solve a system of nonlinear differential equations, which appears in the line search process in the CCM algorithm. The modified algorithm was tested and the analytical solution was verified using nonlinear CHPED optimization problems, thereby demonstrating the effectiveness of the algorithm. The CCM methods proved numerically stable and, in the case of nonlinear programs, produced solutions with unprecedented accuracy within a reasonable time.     

Investigation of assumptions and approximations in the virtual fields method for a viscoplastic material model

The Virtual Fields Method (VFM) is an inverse technique used for parameter estimation and calibration of constitutive models. Many assumptions and approximations—such as plane stress, incompressible plasticity, and spatial and temporal derivative calculations—are required to use VFM with full‐field deformation data, for example, from Digital Image Correlation (DIC). This work presents a comprehensive discussion of the effects of these assumptions and approximations on parameters identified by VFM for a viscoplastic material model for 304L stainless steel. We generated synthetic data from a Finite‐Element Analysis (FEA) in order to have a reference solution with a known material model and known model parameters, and we investigated four cases in which successively more assumptions and approximations were included in the data. We found that VFM is tolerant to small deviations from the plane stress condition in a small region of the sample, and that the incompressible plasticity assumption can be used to estimate thickness changes with little error. A local polynomial fit to the displacement data was successfully employed to compute the spatial displacement gradients. The choice of temporal derivative approximation (i.e., backwards difference versus central difference) was found to have a significant influence on the computed rate of deformation and on the VFM results for the rate‐dependent model used in this work. Finally, the noise introduced into the displacement data from a stereo‐DIC simulator was found to have negligible influence on the VFM results. Evaluating the effects of assumptions and approximations using synthetic data is a critical first step for verifying and validating VFM for specific applications. The results of this work provide the foundation for confidently using VFM for experimental data.     

Correspondence analysis and establishment of evaluation model of classification performance indices for a turbo air classifier

The operational parameters of a turbo air classifier including feeding speed, rotor cage's rotary speed and air inlet velocity affect its classification performance directly, such as cut size, classification precision, classification efficiency, fine powder yield, particle fineness and degree of dispersion. Current methods of optimizing operational parameters and improving the classification performance of a turbo air classifier are almost single objective decision only for one of the classification performance indices. In this paper, the multi‐objective programming (MOP) model on classification performance for a turbo air classifier is established to evaluate these performance indices comprehensively and achieve optimal classification performance. To minimize the effect of repeatability within these classification performance indices, correspondence analysis is applied to determine the evaluation indices of this MOP model. According to correspondence analysis on the fine talc classification experimental data as well as the calcium carbonate classification experimental data, there is a very strong correlation between cut size and D90; there is also a very strong correlation between cut size and fine powder yield. Thus D90 and fine powder yield are filtered out and they aren't discussed in the evaluation model. The variation coefficient method is introduced to calculate weights of the evaluation function, and the dimensionless transformation method is used to eliminate the effects of different dimension. Thus, the optimal solution among the experimental data is obtained through solving the evaluation function. For the talc classification experiments, the optimal operational parameter combinations are: the feeding speed is 40 kg · h^–1, the air inlet velocity is 5 m · s^–1 and the rotor cage's rotary speed is 1200 ? min^–1. The classification performance indices are: cut size is 16.5 μm, classification precision index is 0.59, Newton classification efficiency is 57% and degree of dispersion is 2.13. For the calcium carbonate classification experiments, the optimal operational parameter combinations are: the feeding speed is 92 kg · h^–1, the air inlet velocity is 12 m · s^–1 and the rotor cage's rotary speed is 1200 ? min^–1. The classification performance indices are: cut size is 31.4 μm, classification precision index is 0.74, Newton classification efficiency is 74% and degree of dispersion is 1.27. This evaluation model avoids the limitation of evaluation for the single classification performance index and incomplete information got by the means of single factor experiment of operational parameters. It also provides the quantitative evaluating criteria for classification performance of a turbo air classifier, which offers a theoretical basis for effective production. This multi‐objective programming optimizing method and evaluation model on classification performance can be applied to other dynamic air classifiers as well.