表面细分的最优方法的分析与设计

基于模型上采集的非组织的样本点数据,给出了一个非线性至少平方的表面细分的完整框架。通过研究和分析三个几何上最优的表面细分的方法：点距离最小、切线距离最小、平方距离最小,来揭示它们的相交性与稳定性,以及非线性约束最优化的内部联系。对于点距离最小方法的分析,它是切线下降的变体,因此,只有线性相交。对于切线距离最小方法,它是接近二次相交零余留的问题,也有可能没有相交。平方距离最小方法,可以通过牛顿公式得到,并且是三种方法中相对最优的。通过对这三种方法的研究,来保证表面细分稳定地相交,且解决了对最优方法的争议。     

Hammerstein system identification using nuclear norm minimization

This paper presents a new method for the identification of Hammerstein systems. The parameter estimation problem is formulated as a rank minimization problem by constraining a finite dimensional time dependency between signals. Due to the unknown intermediate signal, the rank minimization problem cannot be solved directly. Thus, the rank minimization problem is reformulated as an intermediate signal construction problem. The main assumption used in this paper is that static nonlinearity is monotonically non-decreasing in order to guarantee a unique combination of a static nonlinear block and a Finite Impulse Response (FIR) linear block. The rank minimization is then relaxed to a convex optimization problem using a nuclear norm. The main contribution of this paper is that the proposed method extends the rank minimization approach to Hammerstein system identification, and does not need a bilinear parametrization and singular value decomposition (SVD), which are commonly used in two-step approaches for Hammerstein system identification.     

结合小波变换的SFS最小化算法研究

提出了一种结合小波变换的从明暗恢复三维形状的最小化方法,该算法利用图像小波变换各个子频段的不同频率特性和方向特性,分别采用不同的算法重构。在图像被分解后的低频区域采用小波直接提取自然条纹相位,高频区域使用最小化方法重构。这种方法在低频区域避免了SFS最小化方法的假设条件,而高频区域又发挥了它对细节部分重构的优势。实验结果表明该算法比单独使用最小化方法的误差要小。     

A least-squares method with direct minimization for the solution of the breakage–coalescence population balance equation

A least-squares method with a direct minimization algorithm is introduced to solve the non-linear population balance equation that consists of both breakage and coalescence terms. The least-squares solver, direct minimization solver together with a finite difference solver are implemented for comparisons. It is shown that the coalescence term introduces a strong non-linear behavior which can affect the robustness of the numerical solvers. In the comparison with the least-squares method, the direct minimization method is proved to be capable of producing equally accurate results, while its formulation is better conditioned. In the case of a non-linear population balance equation system, the direct minimization method converges faster than the standard least-squares method.     

Multi-material topology optimization for practical lightweight design

Topology optimization is one of the most effective tools for conducting lightweight design and has been implemented across multiple industries to enhance product development. The typical topology optimization problem statement is to minimize system compliance while constraining the design space to an assumed volume fraction. The traditional single-material compliance problem has been extended to include multiple materials, which allows increased design freedom for potentially better solutions. However, compliance minimization has the limitations for practical lightweight design because compliance lacks useful physical meanings and has never been a design criterion in industry. Additionally, the traditional compliance minimization problem statement requires volume fraction constraints to be selected a priori; however, designers do not know the optimized balance among materials. In this paper, a more practical method of multi-material topology optimization is presented to overcome the limitations. This method seeks the optimized balance among materials by minimizing the total weight while satisfying performance constraints. This paper also compares the weight minimization approach to compliance minimization. Several numerical examples prove the success of weight minimization and demonstrate its benefit over compliance minimization.     

Design and analysis of optimization methods for subdivision surface fitting

We present a complete framework for computing a subdivision surface to approximate unorganized point sample data, which is a separable nonlinear least squares problem. We study the convergence and stability of three geometrically-motivated optimization schemes and reveal their intrinsic relations with standard methods for constrained nonlinear optimization. A commonly-used method in graphics, called point distance minimization, is shown to use a variant of the gradient descent step and thus has only linear convergence. The second method, called tangent distance minimization, which is well-known in computer vision, is shown to use the Gauss-Newton step, and thus demonstrates near quadratic convergence for zero residual problems but may not converge otherwise. Finally, we show that an optimization scheme called squared distance minimization, recently proposed by Pottmann et al., can be derived from the Newton method. Hence, with proper regularization, tangent distance minimization and squared distance minimization are more efficient than point distance minimization. We also investigate the effects of two step size control methods -- Levenberg-Marquardt regularization and the Armijo rule -- on the convergence stability and efficiency of the above optimization schemes.     

Modification of binary optimization algorithm and use small digit capacity numbers

The article deals with the neural minimization of the quadratic functional in a space of binary variables. A modified minimization algorithm based on the discretization method is offered to tackle the problem. The use of the algorithm is shown to allow a smaller amount of computations.     

有限识别器的最小化方法

给出确定型有限识别器最小化的一种方法,并给出一类非确定型有限识别器最小化的方法。     

An easy method to derive EOQ and EPQ inventory models with backorders

Recently, a cost minimization method to determine the lot size for the EOQ/EPQ models with backorders was published. This method is based on the well-known arithmetic–geometric mean inequality. Although the cost minimization method is correct and interesting, it does not focus on deriving the backorders level. This paper proposes another simple approach. The proposed method finds both the lot size and the backorders level.     

Minimization of logical functions by the method of subimplicants

The method of subimplicants is described for minimization of logical functions that assume no less than three values. The distinctive features of the method are the improvement of results of minimization owing to the extension of gluing conditions and the possibility of minimization of functions that cannot be minimized by traditional methods. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 84–99, May–June, 2000.     

The use of minimization methods in the two-dimensional cross-spring hinge problem

The two-dimensional cross-spring hinge problem is formulated. The resulting boundary value problem for ordinary differential equations is solved by a shooting method combined with a minimization algorithm. A selection of minimization methods is tested, and comparison of their performances is reported. There are also several computational results.     

联合lp/l2,p范数极小化的序列子空间聚类算法

为了有效挖掘序列数据的时空信息,提出联合l_p和l_2,p范数极小化的序列子空间聚类算法.首先,定义依赖于样本距离的权重,构造基于l_2,p范数的时序图,刻画数据在时间维度上的局部相似性.然后,考虑到非凸l_p0l₁范数,能更有效地切断语义无关数据间的联系,所以采用l_p范数度量表示矩阵的稀疏性.最后,通过线性化交替方向法求解优化模型.在视频、运动、人脸数据上的实验表明文中算法的有效性.     

Simultaneous identification of Robin coefficient and heat flux in an elliptic system

In this paper, we shall derive and propose an efficient algorithm for simultaneously reconstructing the Robin coefficient and heat flux in an elliptic system from part of the boundary measurements. The uniqueness of the simultaneous identification is demonstrated. The ill-posed inverse problem is formulated into an output least-squares nonlinear and non-convex minimization with Tikhonov regularization, while the regularizing effects of the regularized system are justified. The Levenberg–Marquardt method is applied to change the non-convex minimization into convex minimization, which will be solved by surrogate functional method so as to get the explicit expression of the minimizer. Numerical experiments are provided to show the accuracy and efficiency of the algorithm.     

全变差最小化在CT图像环状伪影去除中的应用

环状伪影是多种CT图像中普遍存在的一种伪影,主要由像元响应不理想等因素引起。全变差最小化是一种广泛使用的去噪方法,将全变差最小化应用于CT图像,在模拟投影数据中人为添加噪声并重建,使用全变差最小化进行处理,观察图像环状伪影的去除情况,并得出了图像峰值信噪比随全变差最小化次数的变化曲线。     

The Davidon method of solution of the algebraic matrix Riccati equation†

An algorithm is presented for solving the algebraic matrix Riccati equation using the Fletcher-Powell reformulation of Davidon's method of function minimization. The function to be minimized, as well as its gradient vector required by the minimization process, are evaluated in closed-form, thereby preserving the simplicity and stability properties of the minimization procedure. The quadratic convergence of the algorithm is not dependent on the initial choice of the approximate solution.     

Stress-constrained topology optimization with design-dependent loading

The purpose of this paper is to apply stress constraints to structural topology optimization problems with design-dependent loading. A comparison of mass-constrained compliance minimization solutions and stress-constrained mass minimization solutions is also provided. Although design-dependent loading has been the subject of previous research, only compliance minimization has been studied. Stress-constrained mass minimization problems are solved in this paper, and the results are compared with those of compliance minimization problems for the same geometries and loading. A stress-relaxation technique is used to avoid the singularity in the stress constraints, and these constraints are aggregated in blocks to reduce the total number of constraints in the optimization problem. The results show that these design-dependent loading problems may converge to a local minimum when the stress constraints are enforced. The use of a continuation method where the stress-constraint aggregation parameter is gradually increased typically leads to better convergence; however, this may not always be possible. The results also show that the topologies of compliance-minimization and stress-constrained solutions are usually vastly different, and the sizing optimization of a compliance solution may not lead to an optimum.     

Shape from shading using graph cuts

In this paper, we investigate the applicability of graph cuts to the SFS (shape-from-shading) problem. We propose a new semi-global method for SFS using graph cuts. The new algorithm combines the local method proposed by Lee and Rosenfeld [C.H. Lee, A. Rosenfeld, Improved methods of estimating shape from shading using the light source coordinate system, Artif. Intell. 26 (1985) 125-143] and a global method using an energy minimization technique. By employing a new global energy minimization formulation, the convex/concave ambiguity problem of Lee and Rosenfeld's method can be resolved efficiently. A new combinatorial optimization technique, the graph cuts method, is used for the minimization of the proposed energy functional. Experimental results on a variety of synthetic and real-world images show that the proposed algorithm reconstructs the 3-D shape of objects very efficiently.     

基于系数矩阵的极性转换方法及其在MPDRM化简中的应用

针对多输出布尔函数系统混合极性对偶Reed-Muller展开（MPDRM）的极性转换问题, 提出了一种基于系数矩阵的极性转换方法。该方法通过分析使用转换矩阵进行极性转换时所需的矩阵运算, 进行子矩阵提取并将复杂的矩阵运算简化为子矩阵间的同或运算, 提高了极性转换速度。在此基础上, 给出了MPDRM精确化简算法, 该算法采用格雷码策略使得极性转换发生在相邻极性值的MPDRM之间, 并以和项数作为主要化简标准, 文字数作为次要化简标准, 通过采用穷举策略搜索极性空间求解最小MPDRM。实验结果表明, 使用文字数作为次要化简标准能够获得更优化的MPDRM, 与基于列表技术的极性转换方法相比, 所提出方法能够缩短精确化简过程49. 5%的时间。     

一个完善的基于判定链表的DFA最小化算法

应用判定链表进行DFA最小化方法中只处理无互相依赖等价状态会造成最小化结果不正确。针对此问题,分析了DFA中状态的k次传递等价、含自回路状态的等价以及互相依赖等价等结构特点,将分析结果应用于DFA最小化算法中,提出了一个完善的基于判定链表的DFA最小化算法。该算法涵盖所有等价状态的链表处理,与传统的分割或合并算法的最小化结果一致,保证了基于判定链表的最小化结果的正确性。     

A Semi-smooth Newton Method for Inverse Problem with Uniform Noise

In this paper we study inverse problems where observations are corrupted by uniform noise. By using maximum a posteriori approach, an \(L_\infty \)-norm constrained minimization problem can be formulated for uniform noise removal. The main difficulty of solving such minimization problem is how to deal with non-differentiability of the \(L_\infty \)-norm constraint and how to estimate the level of uniform noise. The main contribution of this paper is to develop an efficient semi-smooth Newton method for solving this minimization problem. Here the \(L_\infty \)-norm constraint can be handled by active set constraints arising from the optimality conditions. In the proposed method, linear systems based on active set constraints are required to solve in each Newton step. We also employ the method of moments (MoM) to estimate the level of uniform noise for the minimization problem. The combination of the proposed method and MoM is quite effective for solving inverse problems with uniform noise. Numerical examples are given to demonstrate that our proposed method outperforms the other testing methods.