Nonsmooth-optimization methods with space expansion are considered as applied to decomposition schemes realized in solving two-stage problems of stochastic programming in the SLP-IOR simulation system.
Nonsmooth-optimization methods with space expansion are considered as applied to decomposition schemes realized in solving two-stage problems of stochastic programming in the SLP-IOR simulation system.
This paper considers a procedure of two-stage stochastic programming in which the performance function to be optimized is replaced by its empirical mean. This procedure converts a stochastic optimization problem into ...
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This paper considers a procedure of two-stage stochastic programming in which the performance function to be optimized is replaced by its empirical mean. This procedure converts a stochastic optimization problem into a deterministic one for which many methods are available. Another strength of the method is that there is essentially no requirement on the distribution of the random variables involved. Exponential convergence for the probability of deviation of the empirical optimum from the true optimum is established using large deviation techniques. Explicit bounds on the convergence rates are obtained for the case of quadratic performance functions. Finally, numerical results are presented for the famous news vendor problem and for a resource problem, which lends experimental evidence supporting the exponential convergence.
作者：
Liu, BDTsinghua Univ
Dept Math Sci Uncertain Syst Lab Beijing 100084 Peoples R China
By fuzzy random programming, we mean the optimization theory dealing with fuzzy random decision problems. This paper presents a new concept of chance of fuzzy random events and then constructs a general framework of f...
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By fuzzy random programming, we mean the optimization theory dealing with fuzzy random decision problems. This paper presents a new concept of chance of fuzzy random events and then constructs a general framework of fuzzy random chance-constrained programming (CCP). We also design a spectrum of fuzzy random simulations for computing uncertain functions arising in the area of fuzzy random programming. To speed up the process of handling uncertain functions, we train a neural network to approximate uncertain functions based on the training data generated by fuzzy random simulation. Finally, we integrate fuzzy random simulation, neural network, and genetic algorithm to produce a more powerful and effective hybrid intelligent algorithm for solving fuzzy random programming models and illustrate its effectiveness by some numerical examples.
By uncertain programming we mean the optimization theory in generally uncertain (random, fuzzy, fuzzy random, grey, etc.) environments. Three broad classes of uncertain programming are expected value models and chance...
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By uncertain programming we mean the optimization theory in generally uncertain (random, fuzzy, fuzzy random, grey, etc.) environments. Three broad classes of uncertain programming are expected value models and chance-constrained programming as well as dependent-chance programming. In order to solve general uncertain programming models, a simulation-based genetic algorithm is also documented. Finally some applications and further research problems appearing in this area are posed. (C) 2001 Elsevier Science Inc. All rights reserved.
作者：
Liu, BDTsinghua Univ
Dept Math Sci Uncertain Syst Lab Beijing 100084 Peoples R China
This paper presents the concepts of uncertain environment, event, chance function and principle of uncertainty for fuzzy random decision systems, thus offering a theoretical framework of fuzzy random dependent-chance ...
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This paper presents the concepts of uncertain environment, event, chance function and principle of uncertainty for fuzzy random decision systems, thus offering a theoretical framework of fuzzy random dependent-chance programming. A hybrid intelligent algorithm is applied to solving fuzzy random dependent-chance programming models. Some numerical examples are also provided to illustrate the effectiveness of hybrid intelligent algorithm.
We present an algorithm for solving stochastic integer programming problems with recourse, based on a dual decomposition scheme and Lagrangian relaxation. The approach can be applied to multi-stage problems with mixed...
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We present an algorithm for solving stochastic integer programming problems with recourse, based on a dual decomposition scheme and Lagrangian relaxation. The approach can be applied to multi-stage problems with mixed-integer variables in each time stage. Numerical experience is presented for some two-stage test problems. (C) 1999 Elsevier Science B.V. All rights reserved.
We survey structural properties of and algorithms for stochastic integer programming models, mainly considering linear two-stage models with mixed-integer recourse (and their multi-stage extensions).
We survey structural properties of and algorithms for stochastic integer programming models, mainly considering linear two-stage models with mixed-integer recourse (and their multi-stage extensions).
Sampling and decomposition constitute two of the most successful approaches for addressing large-scale problems arising in statistics and optimization, respectively. In recent years, these two approaches have been com...
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Sampling and decomposition constitute two of the most successful approaches for addressing large-scale problems arising in statistics and optimization, respectively. In recent years, these two approaches have been combined for the solution of large-scale stochastic linear programming problems. This paper presents the algorithmic motivation for such methods, as well as a broad overview of issues in algorithm design. We discuss both basic schemes as well as computational enhancements and stopping rules. We also introduce a generalization of current algorithms to handle problems with random recourse.
stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition. We review some new developments in cutting plane methods, augmented Lagrangian and splittin...
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stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition. We review some new developments in cutting plane methods, augmented Lagrangian and splitting methods for linear multi-stage stochastic programming problems.
作者：
Mulvey, JMPrinceton Univ
Dept Operat Res & Financial Engn Bendheim Ctr Finance Princeton NJ 08544 USA
Optimization models are effective for solving significant problems in finance, including long-term financial planning and other portfolio problems. Prominent examples include: asset-liability management for pension pl...
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Optimization models are effective for solving significant problems in finance, including long-term financial planning and other portfolio problems. Prominent examples include: asset-liability management for pension plans and insurance companies, integrated risk management for intermediaries, and long-term planning for individuals. Several applications will be briefly mentioned. Three distinct approaches are available for solving multi-stage financial optimization models: 1) dynamic stochastic control, 2) stochastic programming, and 3) optimizing a stochastic simulation model. We briefly review the pros and cons of these approaches, discuss further applications of financial optimization, and conclude with topics for future research.
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