Second-order necessary optimality conditions for domain optimization problems of the Neumann type

In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987.     

Value functions,domination cones and proper efficiency in multicriteria optimization

In the absence of a clear objective value function, it is still possible in many cases to construct a domination cone according to which efficient (nondominated) solutions can be found. The relations between value functions and domination cones and between efficiency and optimality are analyzed here. We show that such cones must be convex, strictly supported and, frequently, closed as well. Furthermore, in most applications potential optimal solutions are equivalent to properly efficient points. These solutions can often be produced by maximizing with respect to a class of concave functions or, under convexity conditions, a class of affine functions.     

An extended continuous Newton method

This paper describes a numerical realization of an extended continuous Newton method defined by Diener. It traces a connected set of locally one-dimensional trajectories which contains all critical points of a smooth functionf: ⁿ . The results show that the method is effectively applicable.The authors would like to thank L. C. W. Dixon for pointing out some errors in the original version of this paper and for several suggestions of improvements.     

On consistency of bounding operations in deterministic global optimization

This technical comment refers to the discussion of strong consistency of several bounding procedures in Lemma 2.1 and Proposition 2.1 of Ref. 1. A necessary clarification is given of the notion of convergence _q in Lemma 2.1, and a derivation of Proposition 2.1 is presented that includes a new and simple consistency proof of the classical bounding by convex envelopes used in many branch-and-bound procedures.     

Random tunneling by means of acceptance-rejection sampling for global optimization

Any global minimization algorithm is made by several local searches performed sequentially. In the classical multistart algorithm, the starting point for each new local search is selected at random uniformly in the region of interest. In the tunneling algorithm, such a starting point is required to have the same function value obtained by the last local minimization. We introduce the class of acceptance-rejection based algorithms in order to investigate intermediate procedures. A particular instance is to choose at random the new point approximately according to a Boltzmann distribution, whose temperatureT is updated during the algorithm. AsT 0, such distribution peaks around the global minima of the cost function, producing a kind of random tunneling effect. The motivation for such an approach comes from recent works on the simulated annealing approach in global optimization. The resulting algorithm has been tested on several examples proposed in the literature.     

A theoretical approximation scheme for Stackelberg problems

We consider the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game. We present a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems. From a practical point of view, we also give some results for asymptotically Stackelberg approximating sequences and for problems with perturbed constraints.This paper is based upon results first presented at Journées Fermat: Mathematics for Optimization, Toulouse, France, May 1985.     

Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.     

CuO—ZnO／Al2O3—TiO2催化剂中TiO2的结构和电子效应

采用XPS,XRD,TPR,TPD和指标反应等方法研究了TiO_2在负载型CuO-ZnO/Al_2O_3-TiO_2催化剂中所起的作用.发现TiO_2起双重作用,即结构效应和电子效应,TiO_2的结构效应主要表现为它改善了CuO在载体上的分布.TiO_2的电子效应表现为它对Cu~0具有吸电子的作用,从而削弱了Cu和S之间的吸附力,使S容易脱除.另外,部分还原形成的Ti~(3+)具有促进CuS中的Cu~(2+)还原为Cu~0的能力,TiO_2的上述效应的综合结果使催化剂的抗硫中毒性能大大增强.     

Intrinsic field theory of chemical reactions

An intrinsic principle of least action is presented for the intrinsic dynamism of chemical reactions. Then, as the stationary trajectory, a meta-IRC (intrinsic reaction coordinate) draws a geodesic curve in a rigged Riemannian space. This establishes a geodesic law for the intrinsic dynamism. Moreover, a diagrammatic perturbation theory is formulated for the intrinsic dynamism, and a dynamical interaction between a chemically reacting system and a background system is investigated. Then, the structural stability of the system is discussed using a new concept of the dynamical potential field. An example is given in order to elucidate the present theory.Dedicated to Prof. Hermann Hartmann on the occasion of his 65th birthday.     

晶化温度对中孔分子筛（M41S）结构转变的影响

在低表面活性剂浓度及低表面活性剂与氧化硅比的条件下，研究了十六烷基三甲基溴化铵－硅酸钠体系中晶化温度对中孔分子筛Ｍ４１Ｓ材料结构转变的影响。结果有，晶化温度提高至１３５℃改变了原六方晶相ＭＣＭ－４１的结构，晶化温度提高到１５０℃后，中孔结构六方ＭＣＭ－４１晶格转变为变不稳定的层状相，