Substrate issues for the growth of mercury cadmium telluride

Close lattice matching and lattice compatibility with mercury cadmium telluride (MCT) make CdTe and related alloys ideal substrate materials for growth of MCT layers for the purpose of making high-performance second-generation infrared detectors. However, the limitations in the properties of CdTe and the difficulties in its bulk growth have prompted extensive research in the area of alternative substrates. Some basic relevant characteristics of substrates such as sapphire, GaAs, and silicon are compared and the possibilities and problems associated with each material are analyzed in the light of the most recent results in the field.     

Enlarging the region of convergence of Newton's method for constrained optimization

In this paper, we consider Newton's method for solving the system of necessary optimality conditions of optimization problems with equality and inequality constraints. The principal drawbacks of the method are the need for a good starting point, the inability to distinguish between local maxima and local minima, and, when inequality constraints are present, the necessity to solve a quadratic programming problem at each iteration. We show that all these drawbacks can be overcome to a great extent without sacrificing the superlinear convergence rate by making use of exact differentiable penalty functions introduced by Di Pillo and Grippo (Ref. 1). We also show that there is a close relationship between the class of penalty functions of Di Pillo and Grippo and the class of Fletcher (Ref. 2), and that the region of convergence of a variation of Newton's method can be enlarged by making use of one of Fletcher's penalty functions.This work was supported by the National Science Foundation, Grant No. ENG-79-06332.     

逻辑函数的减-非和除-非展开式的最小化方法

讨论了布尔减和布尔除的定义以及逻辑函数在布尔减及非运算、布尔除及非运算完备集中的展开,给出了减-非和除-非逻辑函数的化简公式.在此基础上提出了减-非和除-非逻辑函数的代数化简法以及图形化简法,并给出了化简实例.实例验证了上述化简方法的有效性.     

Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model

In many applications materials are modeled by a large number of particles (or atoms) where any one of particles interacts with all others. Near or nearest neighbor interaction is expected to be a good simplification of the full interaction in the engineering community. In this paper we shall analyze the approximate error between the solution of the simplified problem and that of the full-interaction problem so as to answer the question mathematically for a one-dimensional model. A few numerical methods have been designed in the engineering literature for the simplified model. Recently much attention has been paid to a finite-element-like quasicontinuum (QC) method which utilizes a mixed atomistic/continuum approximation model. No numerical analysis has been done yet. In the paper we shall estimate the error of the QC method for this one-dimensional model. Possible ill-posedness of the method and its modification are discussed as well.

     

Gauss-seidel method for least-distance problems

In this paper, we reformulate the least-distance problems with bounded inequality constraints as an unconstrained convex minimization problem, which is equivalent to a system of piecewise linear equationsA(a+A ^T y) _c ^d =b. The proposed Gauss-Seidel method for solving the problems is easy to implement and behaves very well when the number of rows ofA is much less than the number of columns ofA. Moreover, we prove that the Gauss-Seidel method has a linear convergence rate.The authors would like to thank Jinshui Qin who did some preliminary numerical testing for their research.     

A rapidly convergent five-point algorithm for univariate minimization

This paper presents an algorithm for minimizing a function of one variable which uses function, but not derivative, values at five-points to generate each iterate. It employs quadratic and polyhedral approximations together with a safeguard. The basic method without the safeguard exhibits a type of better than linear convergence for certain piecewise twice continuously differentiable functions. The safeguard guarantees convergence to a stationary point for very general functions and preserves the better than linear convergence of the basic method.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.Research sponsored by the Institut National de Recherche en Informatique et Automatique, Rocquencourt, France, and by the Air Force Office of Scientific Research, Air Force System Command, USAF, under Grant Number AFOSR-83-0210.Research sponsored, in part, by the Institut National de Recherche en Informatique et Automatique, Rocquencourt, France.     

Some remarks on computer-aided design of optical lens systems

Computer-aided design of optical lens systems implies the solution of an optimization problem of large dimension. To apply a local algorithm, we want to know a starting point within a small neighborhood of the desired system. For a given task, the designer is not able to define a suitable starting point. In this paper, we describe a global optimization algorithm which uses the principles of biological evolution with the aim of locating an adequate starting point for a local correction routine.This work was supported by the Department of Mathematics, Friedrich Schiller University, Jena, GDR, in cooperation with the research center of VEB Kombinat Carl Zeiss, Jena, GDR. The authors are indebted to Dr. L. C. W. Dixon for discussions of the topic.     

A linear hyperbolic system and an optimal control problem

We prove a theorem of existence, uniqueness, and continuous dependence for a linear hyperbolic system with Darboux-type conditions under assumptions on the coefficients, which are in a sense the most general possible. Moreover, an application of this result to an optimal control problem is given.     

A rank-one algorithm for unconstrained function minimization

A rank-one algorithm is presented for unconstrained function minimization. The algorithm is a modified version of Davidon's variance algorithm and incorporates a limited line search. It is shown that the algorithm is a descent algorithm; for quadratic forms, it exhibits finite convergence, in certain cases. Numerical studies indicate that it is considerably superior to both the Davidon-Fletcher-Powell algorithm and the conjugate-gradient algorithm.     

A modification of Armijo's step-size rule for negative curvature

Armijo's step-size procedure for function minimization is modified to include second derivative information. Accumulation points using this procedure are shown to be stationary points with positive semi-definite Hessian matrices.This research was supported by the United States Army Research Office.