摘要:

This paper proposes an approximation approach to the solution of chance-constrained stochastic programming problems. The results rely in a fundamental way on the theory of convergence of sequences of measurable multifunctions. Particular results are presented for stochastic linear programming problems.

ISSN:0090-9491    

DOI:10.1080/17442508308833272

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

In most stochastic decision problems one has the opportunity to collect information that would partially or totally eliminate the inherent uncertainty. One wishes to compare the cost and value of such information in terms of the decision maker's preferences to determine an optimal information gathering plan. The calculation of the value of information generally involves oneor more stochastic recourse problems as well as one or more expected value distribution problems. The difficulty and costs of obtaining solutions to these problems has led to a focus on the development of upper and lower bounds on the various subproblems that yield bounds on the value of information. In this paper we discuss published and new bounds for static problems with linear and concave preference functions for partial and perfect information. We also provide numerical examples utilizing simple production and investment problems that illustrate the calculations involved in the computation of the various bounds and provide a setting for a comparison of the bounds that yields some tentative guidelines for their use. The bounds compared are the Jensen's Inequality bound,the Conditional Jensen's Inequality bound and the Generalized Jensen and Edmundson-Madansky bounds.

ISSN:0090-9491    

DOI:10.1080/17442508308833273

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

In this paper we describe an algorithm for solving stochastic programs with simplerecourse, i.e.,generated by a linear programming problem with stochastic coefficients and a specific loss function (piecewise linear) associated with discrepancies observed between the output (Tx) and the resource vector. We show that this class of problems can actually be solved with about the same efficiency as solving linear programs of the same size. We first give a method for the discrete case and then indicate how recent approximation results can be used to obtain solutions whenthe random variables have a continuous distribution.

ISSN:0090-9491    

DOI:10.1080/17442508308833274

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

In this paper we generalize Vere-JonesR-theory from irreducible to reducible nonnegative matrices of countably infinite dimension. We discuss excessive functions and eigenvectors associated with the convergence parameterR. Furthermore we show how generalized eigenvectors associated withRcan be constructed. Under special conditions related to strong ergodicity in Markov chains, these generalized eigenvectors can be chosen nonnegative. The results are extended to sets of nonnegative matrices which often appear in optimization problems (e.g. Markov decision chains, Leontief substitution systems).

ISSN:0090-9491    

DOI:10.1080/17442508308833275

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

In this paper we consider deterministic and stochastic versions of discrete time analogs of optimization problems of the Bolza type. The functionals are assumed to be convex, but we make no differentiability assumptions and allow for the explicit or implicit presence of constraints both on the state xtand the increments△xt. The deterministic theory serves to set the stage for the stochastic problem. We obtain optimality conditions that are always sufficient and which are also necessary if the given problem satisfies a strict feasibility condition and, in the stochastic case, a bounded recourse condition. This is a new condition that bypasses the uniform boundedness restrictions encountered in earlier work on related problems.

ISSN:0090-9491    

DOI:10.1080/17442508308833276

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/174425088308833270

出版商:Gordon and Breach Science Publishers S. A.    

年代:1983

数据来源: Taylor