Optimal control for semilinear evolutionary variational bilateral problem

This paper is concerned with an optimal control problem for some semilinear evolutionary variational inequalities associated with bilateral constraints. The control domain is a general separable metric space and has no algebraic structure, in particular, it is not necessarily convex. Existence and optimality conditions of optimal pairs are established.     

一类具年龄结构种群动力系统的最优控制

研究一类具年龄结构种群线性动力系统的最优控制问题 .由Mazur’s定理 ,我们证明了最优控制问题 (OH)最优解的存在性 ,同时借助于法锥概念 ,我们还得到了最优控制问题 (OH)最优解存在的必要条件     

A NOTE ON THE BACKWARD ERRORS FOR INVERSE EIGENVALUE PROBLEMS

In this note,we consider the backward errors for more general inverse eigenvalus prob-lems by extending Sun‘‘‘‘s approach.The optimal backward errors defined for diagonal-ization matrix inverse eigenvalue problem with respect to an approximate solution,and the upper and lower bounds are derived for the optimal backward errors.The results may be useful for testing the stability of practical algorithms.     

多目标模糊系数规划

在单目标模糊系数规划的理论基础上，对多目标模糊系数规划进行讨论，在以目标间的协调程度尽可能大为最优性条件的要求下提出多目标模糊系数规划最优解的定义，并给出一种可行的求解方法。     

Optimal rigid body motions,part 2: Minimum time solutions

The time-optimal control of rigid-body angular rates is investigated in the absence of direct control over one of the angular velocity components. The existence of singular subarcs in the time-optimal trajectories is explored. A numerical survey of the optimality conditions reveals that, over a large range of boundary conditions, there are in general several distinct extremal solutions. A classification of extremal solutions is presented, and domains of existence of the extremal subfamilies are established in a reduced parameter space. A locus of Darboux points is obtained, and global optimality of the extremal solutions is observed in relation to the Darboux points. The continuous dependence of the optimal trajectories with respect to variations in control constraints is noted, and a procedure to obtain the time-optimal bang-bang solutions is presented.This work was supported in part by DARPA under Contract No. ACMP-F49620-87-C-0016, by SDIO/IST under Contract No. F49620-87-C0088, and by Air Force Grant AFOSR-89-0001.     

Optimization of the Production Medium for Biosynthesis of Antifungal Antibiotic Ak-111-81 by Phosphate-Deregulated Mutant of <Emphasis Type="Italic">Streptomyces hygroscopicus</Emphasis>

Experimental mathematical designs were applied for optimization of a nutrient medium for biosynthesis of the antifungal antibiotic AK-111-81 by phosphate-deregulated mutant of Streptomyces hygroscopicus 111-81. Antifungal antibiotic AK-111-81 possesses well-expressed activity against Fusarium graminearum and other phytopathogenic fungi. The level of the production of the antibiotic AK-111-81 on this medium is more than three times higher than on the initial medium. The optimized quantitative composition of the nutrient culture media is (g/l): glucose, 20; soy meal, 18; ammonium succinate, 3; CaCO₃, 1.     

Optimal decay rates and the selfadjoint property in overdamped systems

We deal with abstract linear strongly damped wave equations. In the so-called overdamped regime we show the occurrence of two interesting phenomena. The first is the existence of an explicit special inner product which makes the problem selfadjoint. The second is an improvement of the decay rate for more regular solutions that will be of an exponential-polynomial type. Furthermore, we prove the optimality of this decay rate.     

Optimal Distributed Dynamic Advertising

We propose a novel approach to modeling advertising dynamics for a firm operating over a distributed market domain based on controlled partial differential equations of the diffusion type. Using our model, we consider a general type of finite-horizon profit maximization problem in a monopoly setting. By reformulating this profit maximization problem as an optimal control problem in infinite dimensions, we derive sufficient conditions for the existence of its optimal solutions under general profit functions, as well as state and control constraints, and provide a general characterization of the optimal solutions. Sharper, feedback-form characterizations of the optimal solutions are obtained for two variants of the general problem. The first author gratefully acknowledges financial support by the NSF, the DAAD, the SFB 611 (Bonn), and the Max-Planck-Institut für Mathematik (Leipzig) through an IPDE fellowship.     

人才管理的一个决策模型

本文应用随机过程理论，结合最优化方法．给出一个企业雇员素质管理的Ｍａｒｋｏｖ决策模型．     

Optimality conditions for state constrained nonlinear control problems

The problem of optimal control of nonlinear control and state constrained control problems, where the state constraint may involve differential operators and the cost functionals may be nonsmooth, is studied. For this class of problems, necessary optimality conditions using techniques from infinite dimensional optimization theory adapted to the framework of control problems are derived. It is shown that the underlying structure admits a considerable relaxation of the classical constraint qualifications. The theory then is applied to examples of various nonlinear elliptic equations and state constraints.