A population global optimization algorithm to solve the image alignment problem in electron crystallography

Knowledge of the structure of biological specimens is critical to understanding their function. Electron crystallography is an electron microscopy (EM) approach that derives the 3D structure of specimens at high-resolution, even at atomic detail. Prior to the tomographic reconstruction, the images taken from the microscope have to be properly aligned. Traditional alignment methods in electron crystallography are based on a phase residual function to be minimized by inefficient exhaustive search procedures. This work addresses this minimization problem from an evolutionary perspective. Universal Evolutionary Global Optimizer (UEGO), an evolutionary multimodal optimization algorithm, has been applied and evaluated for the task of image alignment in this field. UEGO has turned out to be a promising technique alternative to the standard methodology. The alignments found out by UEGO show high levels of accuracy, while reducing the number of function evaluations by a significant factor with respect to the standard method.     

Discrete global descent method for discrete global optimization and nonlinear integer programming

A novel method, entitled the discrete global descent method, is developed in this paper to solve discrete global optimization problems and nonlinear integer programming problems. This method moves from one discrete minimizer of the objective function f to another better one at each iteration with the help of an auxiliary function, entitled the discrete global descent function. The discrete global descent function guarantees that its discrete minimizers coincide with the better discrete minimizers of f under some standard assumptions. This property also ensures that a better discrete minimizer of f can be found by some classical local search methods. Numerical experiments on several test problems with up to 100 integer variables and up to 1.38 × 10¹⁰⁴ feasible points have demonstrated the applicability and efficiency of the proposed method.     

具有生产性与福利性公共支出的随机内生增长模型

文章建立一个随机内生增长模型来阐明主要政策参数对经济增长与社会福利的影响.若对生产函数、效用函数、偏好及随机干扰作一些特殊的假设,我们证明了主要政策参数的均衡值能被模型参数唯一决定.进一步我们还得到了期望增长率与储蓄的清晰解.文章的最后,我们证明了政府支出直接影响个体决策者的决策:即提高经济增长率将减少福利;反之,增加福利将减少增长率.     

基于增广Lagrange函数的RQP方法

Recursive quadratic programming is a family of techniques developd by Bartholomew-Biggs and other authors for solving nonlinear programming problems.This paperdescribes a new method for constrained optimization which obtains its search di-rections from a quadratic programming subproblem based on the well-known aug-mented Lagrangian function.It avoids the penalty parameter to tend to infinity.We employ the Fletcher‘s exact penalty function as a merit function and the use of an approximate directional derivative of the function that avoids the need toevaluate the second order derivatives of the problem functions.We prove that thealgorithm possesses global and superlinear convergence properties.At the sametime, numerical results are reported.     

从最优规模到更大的最优规模--理性企业规模的线性优化

企业效益是以规模为基础的，不同企业最优规模及达到的方式不同。本讨论了企业为获得最优效益，在理性、线性的最优规模下处理过剩资源，单纯的规模扩张及价格与产量关系线性时的规模扩张。指出在初步最优规模，无过剩资源时，单纯的规模扩张以资源同增长的方式最优；在价格与产量关系线性时，企业有最优扩张系数，最大的最优规模。     

An experimental analysis of a population based approach for global optimization

In this paper we perform a computational analysis of a population based approach for global optimization, Population Basin Hopping (PBH), which was proven to be very efficient on very challenging global optimization problems by the authors (see ). The experimental analysis aims at understanding more deeply how the approach works and why it is successful on challenging problems.     

Corrected mirror systems with double reflection

We propose objectives consisting of two mirrors with central holes for passage of a light beam. The optical layout ensures multiple reflection of rays from both mirrors. We consider several approaches to calculating the design parameters for which three and four aberrations do not occur. The objectives can be used in optical devices operating in the UV and IR regions of the spectrum. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 267–270, March–April, 2007.     

Bivariate Free Knot Splines

We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature.     

Frame-Based Ray Search Algorithms in Unconstrained Optimization

This paper describes a class of frame-based direct search methods for unconstrained optimization without derivatives. A template for convergent direct search methods is developed, some requiring only the relative ordering of function values. At each iteration, the template considers a number of search steps which form a positive basis and conducts a ray search along a step giving adequate decrease. Various ray search strategies are possible, including discrete equivalents of the Goldstein–Armijo and one-sided Wolfe–Powell ray searches. Convergence is shown under mild conditions which allow successive frames to be rotated, translated, and scaled relative to one another.