First-Order Necessary Conditions of Optimality for Strongly Monotone Nonlinear Control Problems

Necessary conditions for the optimality of a pair (y*, u*) with respect to the cost functional g(y) + h(u) subject to AyBu + f are given in terms of generalized gradients. Here, g is locally Lipschitz, h is convex, A is a maximal strongly monotone operator, and B is linear. Two examples of applications of our necessary conditions to nonlinear partial differential equations of elliptic type are presented.     

On the Efficiency of a Global Non-differentiable Optimization Algorithm Based on the Method of Optimal Set Partitioning

The examined algorithm for global optimization of the multiextremal non-differentiable function is based on the following idea: the problem of determination of the global minimum point of the function f(x) on the set (f(x) has a finite number of local minima in this domain) is reduced to the problem of finding all local minima and their attraction spheres with a consequent choice of the global minimum point among them. This reduction is made by application of the optimal set partitioning method. The proposed algorithm is evaluated on a set of well-known one-dimensional, two-dimensional and three-dimensional test functions. Recommendations for choosing the algorithm parameters are given.     

Higher-Order Convex Approximations of Young Measures in Optimal Control

The general theory of approximation of (possibly generalized) Young measures is presented, and concrete cases are investigated. An adjoint-operator approach, combined with quasi-interpolation of test integrands, is systematically used. Applicability is demonstrated on an optimal control problem for an elliptic system, together with one-dimensional illustrative calculations of various options.     

Continuous-Time Controlled Markov Chains with Discounted Rewards

This paper studies denumerable state continuous-time controlled Markov chains with the discounted reward criterion and a Borel action space. The reward and transition rates are unbounded, and the reward rates are allowed to take positive or negative values. First, we present new conditions for a nonhomogeneous Q(t)-process to be regular. Then, using these conditions, we give a new set of mild hypotheses that ensure the existence of -optimal (0) stationary policies. We also present a martingale characterization of an optimal stationary policy. Our results are illustrated with controlled birth and death processes.     

ON OPTIMAL ENVIRONMENTAL TAXATION AND ENFORCEMENT: INFORMATION,MONITORING AND EFFICIENCY

ABSTRACT. The purpose of the paper is to contribute to the narrowing of the distance between formal theory and practical environmental policy design. We formulate a general and comprehensive theoretical model in order to take into account the different informational and technological problems which characterize the definition and implementation of environmental taxes in a second best world where there also are distortionary taxes. Having formalized these problems, we present a general model which allows us to discuss the existence of efficient and implementable environmental quality objectives and policy instruments, and to analyze many particular cases.     

“调配问题”的动态规划模型与计算

本给出了调配问题的动态规划模型与计算,该表征更具一般化,且便于计算机计算。     

Convexity of Nonlinear Image of a Small Ball with Applications to Optimization

Let f: XY be a nonlinear differentiable map, X,Y are Hilbert spaces, B(a,r) is a ball in X with a center a and radius r. Suppose f (x) is Lipschitz in B(a,r) with Lipschitz constant L and f (a) is a surjection: f (a)X=Y; this implies the existence of >0 such that f (a)^* yy, yY. Then, if r,/(2L), the image F=f(B(a,)) of the ball B(a,) is convex. This result has numerous applications in optimization and control. First, duality theory holds for nonconvex mathematical programming problems with extra constraint x–a. Special effective algorithms for such optimization problems can be constructed as well. Second, the reachability set for small power control is convex. This leads to various results in optimal control.     

The Bootstrap Methodology in Statistics of Extremes—Choice of the Optimal Sample Fraction

The main objective of statistics of extremes is the prediction of rare events, and its primary problem has been the estimation of the tail index , usually performed on the basis of the largest k order statistics in the sample or on the excesses over a high level u. The question that has been often addressed in practical applications of extreme value theory is the choice of either k or u, and an adaptive estimation of . We shall be here mainly interested in the use of the bootstrap methodology to estimate adaptively, and although the methods provided may be applied, with adequate modifications, to the general domain of attraction of G, , we shall here illustrate the methods for heavy right tails, i.e. for > 0. Special relevance will be given to the use of an auxiliary statistic that is merely the difference of two estimators with the same functional form as the estimator under study, computed at two different levels. We shall also compare, through Monte Carlo simulation, these bootstrap methodologies with other data-driven choices of the optimal sample fraction available in the literature.     

Preconditioned sor methods for generalized least-squares problems

1.IntroductionThegeneralizedleastsquaresproblem,definedasmin(Ax--b)"W--'(Ax--b),(1.1)xacwhereAERm",m>n,bERm,andWERm'misasymmetricandpositivedefinitematrix,isfrequentlyfoundwhensolvingproblemsinstatistics,engineeringandeconomics.Forexample,wegetgeneralizedleastsquaresproblemswhensolvingnonlinearregressionanalysisbyquasi-likelihoodestimation,imagereconstructionproblemsandeconomicmodelsobtainedbythemaximumlikelihoodmethod(of.[1,21).Paige[3,4]investigatestheproblemexplicitly.Hechangestheorig…     

Time-optimal control of a parabolic system with time lags given in the integral form

In this paper the time-optimal control problem for a distributedparabolic system in which time lags appear in the integral formboth in the state equation and in the boundary condition ispresented. The particular properties of the optimal controlare discussed.