Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions,...
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Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original expected recourse function is established.
Practical portfolio investment problems under uncertainty can be modeled well as multiperiod stochastic programs. However, the numerical optimization methods that need to be used to solve such models seriously limit t...
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Practical portfolio investment problems under uncertainty can be modeled well as multiperiod stochastic programs. However, the numerical optimization methods that need to be used to solve such models seriously limit the level of detail in the uncertainty about future asset prices and returns that can be incorporated. Somewhat surprisingly, the question how this necessarily approximate description of the uncertainty should be constructed has received relatively little attention in the stochastic programming literature. Moreover, many of the descriptions that have been used are not arbitrage-free, and therefore inconsistent with modern financial asset-pricing theory. In this paper we will present aggregation methods that tan be used in combination with financial asset-pricing models to obtain a description of the uncertainty that is arbitrage-free, consistent with observed market prices as well as concise enough for a stochastic programming model. Furthermore, we will discuss how these aggregation methods can form the basis of an iterative solution approach.
We apply the techniques of response surface methodology (RSM) to approximate the objective function of a two‐stage stochastic linear program with recourse. In particular, the objective function is estimated, in the r...
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The design, dimensioning and traffic management of an Asynchronous Transfer Mode (ATM) network may be modelled as a hierarchical planning problem at different time-scales - capacity provision/expansion with intervals ...
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The design, dimensioning and traffic management of an Asynchronous Transfer Mode (ATM) network may be modelled as a hierarchical planning problem at different time-scales - capacity provision/expansion with intervals of weeks or months and real-time call routing at the time scale of the connection, which is itself treated in hierarchical order of transmitting calls (sec), bursts (msec) or cells (mu sec). Taking the network topology as given, a chance constrained stochastic programme for integrated services network dimensioning and traffic management is formulated using Hui's notion of effective bandwidth. This allows the removal of probabilistic constraints at the call level and leads to consideration of the network management problem as a linear deterministic multicommodity flow problem. To allow flexibility and easy problem formulation with various objectives and network specifications the decision support tool MODLER is employed. The model described can be used for a prototype software system for future network design and management.
By uncertain programming we mean the optimization theory in generally uncertain (random, fuzzy, fuzzy random, rough, etc.) environments. stochastic programming, fuzzy programming, fuzzy random programming and rough pr...
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ISBN:
(纸本)0780358775;0780358783
By uncertain programming we mean the optimization theory in generally uncertain (random, fuzzy, fuzzy random, rough, etc.) environments. stochastic programming, fuzzy programming, fuzzy random programming and rough programming are subtopics of uncertain programming. This paper provides a brief introduction to uncertain programming, including modeling ideas, hybrid intelligent algorithms, and applications in uncertain decision systems. Some further research problems appearing in this area are also posed.
This paper proposes a data parallel procedure for randomly generating test problems for two-stage quadratic stochastic programming. Multiple quadratic programs in the second stage are randomly generated in parallel. A...
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This paper proposes a data parallel procedure for randomly generating test problems for two-stage quadratic stochastic programming. Multiple quadratic programs in the second stage are randomly generated in parallel. A solution of the quadratic stochastic program is determined by multiple symmetric linear complementarity problems. The procedure allows the user to specify the size of the problem, the condition numbers of the Hessian matrices of the objective functions and the structure of the feasible regions in the first and the second stages. These test problems are used to evaluate three parallel algorithms for multiple quadratic programs and a parallel inexact Newton method for quadratic stochastic programming. Numerical experiments on a Thinking Machine CM-5, Silicon Graphics Power Challenge, and DEC Alpha Server are reported.
Network reliability models for determining optimal network topology have been presented and solved by many researchers. This paper presents some new types of topological optimization model for communication network wi...
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Network reliability models for determining optimal network topology have been presented and solved by many researchers. This paper presents some new types of topological optimization model for communication network with multiple reliability goals. A stochastic simulation-based genetic algorithm is also designed for solving the proposed models. Some numerical examples are finally presented to illustrate the effectiveness of the algorithm. (C) 2000 Elsevier Science Ltd. All rights reserved.
This paper presents a new concept to include uncertainty management in energy and environmental planning models developed in algebraic modeling languages. SETSTOCH is a tool for linking algebraic modeling languages wi...
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This paper presents a new concept to include uncertainty management in energy and environmental planning models developed in algebraic modeling languages. SETSTOCH is a tool for linking algebraic modeling languages with specialized stochastic programming solvers. Its main role is to retrieve from the modeling language a dynamically ordered core model (baseline scenario) that is sent automatically to the stochastic solver. The case presented herein concerns such a study realized with the IEA-MARKAL model used by many research teams around the world.
We apply ideas from stochastic optimization for defining universal portfolios. Universal portfolios are that class of portfolios which an constructed directly from the available observations of the stocks behavior wit...
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We apply ideas from stochastic optimization for defining universal portfolios. Universal portfolios are that class of portfolios which an constructed directly from the available observations of the stocks behavior without any assumptions about their statistical properties. Cover [7] has shown that one can con struct such portfolio using only observations of the past stock prices which generates the same asymptotic wealth growth as the best constant rebalanced portfolio which is constructed with the full knowledge of the future stock market behavior. In this paper we construct universal portfolios using a different set of ideas drawn from nonstationary stochastic optimization. Our portfolios yield the same asymptotic growth of wealth as the best constant rebalanced portfolio constructed with the perfect knowledge of the future and they are less demanding computationally compared to previously known universal portfolios. We also present computational evidence using New York Stock Exchange data which shows, among other things, superior performance of portfolios which explicitly take into account possible nonstationary market behavior.
In this paper we present a parallel method for solving two-stage stochastic linear programs with restricted recourse. The mathematical model considered here can be used to represent several real-world applications, in...
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In this paper we present a parallel method for solving two-stage stochastic linear programs with restricted recourse. The mathematical model considered here can be used to represent several real-world applications, including financial and production planning problems, for which significant changes in the recourse solutions should be avoided because of their difficulty to be implemented. Our parallel method is based on a primal-dual path-following interior point algorithm, and exploits fruitfully the dual block-angular structure of the constraint matrix and the special block structure of the matrices involved in the restricted recourse model. We describe and discuss both message-passing and shared-memory implementations and we present the numerical results collected on the Origin2000. (C) 2000 Elsevier Science B.V. All rights reserved.
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