Optimization methods for computing global minima of nonconvex potential energy functions

The minimization of potential energy functions plays an important role in the determination of ground states or stable states of certain classes of molecular clusters and proteins. In this paper we introduce some of the most commonly used potential energy functions and discuss different optimization methods used in the minimization of nonconvex potential energy functions. A very complete bibliography is also given.Also a researcher at the Army High Performance Computing Research Center, University of Minnesota, Minneapolis, MN 55415     

The simplex method as a global optimizer: A c-programming perspective

In this paper we give a brief account of the important role that the conventional simplex method of linear programming can play in global optimization, focusing on its collaboration with composite concave programming techniques. In particular, we demonstrate how rich and powerful the c-programming format is in cases where its parametric problem is a standard linear programming problem.     

Initial Boundary Value Problem for A Generalized Nonlinear Telegraph Equation with Nonlinear Damping北大核心CSCD

In this paper, the existence and uniqueness of the global generalized solution and the global classical solution of the initial boundary value problem for the generalized nonlinear telegraph equation with nonlinear damping © 2022 Chinese Academy of Sciences. All rights reserved.     

存零约束优化问题的序列二次方法北大核心CSCD

存零约束优化(MPSC)问题是近年来提出的一类新的优化问题,因存零约束的存在,使得常用的约束规范不满足,以至于现有算法的收敛性结果大多不能直接应用于该问题.应用序列二次规划(SQP)方法求解该问题,并证明在存零约束的线性独立约束规范下,子问题解序列的聚点为原问题的Karush-Kuhn-Tucker点.同时为了完善各稳定点之间的关系,证明了强平稳点与KKT点的等价性.最后数值结果表明,序列二次规划方法处理这类问题是可行的.     

一类三阶非线性系统的全局稳定性

本文运用“类比法”，构造了一类三阶非线性系统的李雅普诺夫函数，从而推出了该系统的零解全局渐近稳定的条件。     

Global smooth solutions for a class of parabolic integrodifferential equations

The existence and uniqueness of smooth global large data solutions of a class of quasilinear partial integrodifferential equations in one space and one time dimension are proved, if the integral kernel behaves like near with . An existence and regularity theorem for linear equations with variable coefficients that are related to this type is also proved in arbitrary space dimensions and with no restrictions for .

     

Nonlinear oscillations of second order differential equations of Euler type

We consider the nonlinear equation , where satisfies for , but is not assumed to be sublinear or superlinear. We discuss whether all nontrivial solutions of the equation are oscillatory or nonoscillatory. Our results can be applied even to the case , which is most difficult.

     

Prediction of Oligopeptide Conformations via Deterministic Global Optimization

A deterministic global optimization method is described for identifying the global minimum potential energy conformation of oligopeptides. The ECEPP/3 detailed potential energy model is utilized for describing the energetics of the atomic interactions posed in the space of the peptide dihedral angles. Based on previous work on the microcluster and molecular structure determination [21, 22, 23, 24], a procedure for deriving convex lower bounding functions for the total potential energy function is developed. A procedure that allows the exclusion of domains of the (ø, ) space based on the analysis of experimentally determined native protein structures is presented. The reduced disjoint sub-domains are appropriately combined thus defining the starting regions for the search. The proposed approach provides valuable information on (i) the global minimum potential energy conformation, (ii) upper and lower bounds of the global minimum energy structure and (iii) low energy conformers close to the global minimum one. The proposed approach is illustrated with Ac-Ala4-Pro-NHMe, Met-enkephalin, Leu-enkephalin, and Decaglycine.     

孔结构对铜基甲醇合成催化剂宏观反应速率的影响Ⅰ．未中毒颗粒催化剂

催化剂的宏观反应速率受颗粒内扩散过程的影响，而内扩散过程又取决于催化剂颗粒的孔结构。以铜基甲醇合成催化剂为研究体系，通过改变压片压强和共沉淀条件，制备具有不同孔结构参数（比表面、孔隙率、孔径分布、孔容、颗粒密度、曲折因子）的颗粒催化剂，由反应工程中的扩散－反应方程，按照平行交联孔模型计算有效扩散系数，模拟计算单颗粒催化剂在工业生产条件下的宏观反应速率，从而研究孔结构对未中毒铜基甲醇合成催化剂宏观反应速率的影响。     

Ab initio prediction of helical segments in polypeptides

An ab initio method has been developed to predict helix formation for polypeptides. The approach relies on the systematic analysis of overlapping oligopeptides to determine the helical propensity for individual residues. Detailed atomistic level modeling, including entropic contributions, and solvation/ionization energies calculated through the solution of the Poisson-Boltzmann equation, is utilized. The calculation of probabilities for helix formation is based on the generation of ensembles of low energy conformers. The approach, which is easily amenable to parallelization, is shown to perform very well for several benchmark polypeptide systems, including the bovine pancreatic trypsin inhibitor, the immunoglobulin binding domain of protein G, the chymotrypsin inhibitor 2, the R69 N-terminal domain of phage 434 repressor, and the wheat germ agglutinin.