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Large Deviations of Empirical Estimates in the stochastic programming problem with Nonstationary Observations and Continuous Time

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CYBERNETICS AND SYSTEMS ANALYSIS 2019年第5期55卷 772-777页

作者： Knopov, P. S. Kasitskaya, E. J. Natl Acad Sci VM Glushkov Inst Cybernet Kiev Ukraine

The paper considers a stochastic programming problem with the empirical function constructed based on nonstationary observations and continuous time. A random process, stationary in a narrow sense and satisfying the strong mixing condition is investigated in the problem. The conditions under which the empirical estimate is consistent are given and large deviations of the estimate are considered.

关键词： stochastic programming problem stationary ergodic random process strong mixing condition large deviations

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ON LARGE DEVIATIONS OF EMPIRICAL ESTIMATES IN A stochastic programming problem WITH TIME-DEPENDENT OBSERVATIONS

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CYBERNETICS AND SYSTEMS ANALYSIS 2010年第5期46卷 724-728页

作者： Knopov, P. S. Kasitskaya, E. J. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine

The paper considers a stochastic programming problem with an empirical function constructed based on time-dependent observations. A strictly stationary random sequence that satisfies a strong mixing condition is investigated. The conditions under which an empirical estimate is consistent are given, and large deviations of the estimate are considered.

关键词： stochastic programming problem stationary ergodic random sequence strong mixing condition large deviations

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Asymptotics of statistical estimates in stochastic programming problems with long-range dependent samples

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2002年第1期55卷 37-54页

作者： Wang, LH Nanjing Univ Dept Math Nanjing 210093 Peoples R China

In this paper we investigate the asymptotics of the statistical estimates of the optimal value and the optimal solution in stochastic programming problems, which has long range dependent samples. The asymptotic distri... 详细信息

关键词： asymptotic distribution convergence rate long-range dependence statistical estimates stochastic programming problem

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Co-optimization of energy and reserve in standalone micro-grid considering uncertainties

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ENERGY 2019年 176卷 792-804页

作者： Bahramara, Salah Sheikhahmadi, Pouria Golpir, Hemin Islamic Azad Univ Sanandaj Branch Dept Elect Engn Sanandaj Iran Univ Kurdistan Dept Elect & Comp Engn Sanandaj Iran

The electrical energy systems suffer from several problems of operation including production of greenhouse gas emissions and low energy efficiency in fossil fuel-based power plants as well as high energy losses in transmission and distribution networks. Transition from the traditional centralized power generation into distributed power generation, via distributed energy resources, is introduced as a solution to deal with these problems. Micro-grid concept, as a cluster of distributed energy resources and local loads, is introduced to effectively realize distributed power generation. In standalone mode, micro-grid operator faces uncertainties which should be appropriately tackled into the operation problem formulation. For this purpose, a new decision making framework is proposed in this paper which guarantees optimal scheduling of distributed energy resources to simultaneously provide energy and reserve. The proposed modeling framework, which is visualized through a new risk-based stochastic approach, controls the risk of micro-grid operator in decision-making by Conditional Value at Risk method. Numerical results demonstrates the effectiveness of the proposed framework to model the operation problem of a standalone micro-grid under different uncertainties. Moreover, sensitivity analysis reveals that by increasing the percentage of invoked reserve the expected total cost of micro-grid operator increases to manage the uncertainties. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Renewable energy resources Risk management Standalone micro-grid stochastic programming problem Uncertainty

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A stochastic Nash Equilibrium problem for Medical Supply Competition

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2022年第1-3期193卷 354-380页

作者： Fargetta, Georgia Maugeri, Antonino Scrimali, Laura Univ Catania Catania Italy

In this paper, we study the competition of healthcare institutions for medical supplies in emergencies caused by natural disasters. In particular, we develop a two-stage procurement planning model in a random environment. We consider a pre-event policy, in which each healthcare institution seeks to minimize the purchasing cost of medical items and the transportation time from the first stage, and a recourse decision process to optimize the expected overall costs and the penalty for the prior plan, in response to each disaster scenario. Thus, each institution deals with a two-stage stochastic programming model that takes into account the unmet demand at the first stage, and the consequent penalty. Then, the institutions simultaneously solve their own stochastic optimization problems and reach a stable state governed by the stochastic Nash equilibrium concept. Moreover, we formulate the problem as a variational inequality;both the discrete and the general probability distribution cases are described. We also present an alternative formulation using infinite-dimensional duality tools. Finally, we discuss some numerical illustrations applying the progressive hedging algorithm.

关键词： stochastic programming problem Variational inequality Duality Medical Supplies

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Consistency and Properties of Large Deviations of Empirical Estimates in stochastic Optimization problems for Homogeneous Random Fields under Nonhomogeneous and Homogeneous Observations

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CYBERNETICS AND SYSTEMS ANALYSIS 2021年第1期57卷 16-29页

作者： Knopov, P. S. Kasitskaya, E. J. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Kiev Ukraine

The paper considers a stochastic programming problem with the empirical function constructed from nonhomogeneous observations of a homogeneous random field. The field satisfying the strong mixing condition is investigated in the problem. The conditions whereby the empirical estimate is consistent are given, and large deviations of the estimate for homogeneous observations are estimated.

关键词： stochastic programming problem random field homogeneous in a strict sense nonhomogeneous observations strong mixing condition large deviations

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ON THE CONVERGENCE OF EMPIRICAL ESTIMATES IN problemS OF stochastic programming FOR PROCESSES WITH DISCRETE TIME

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CYBERNETICS AND SYSTEMS ANALYSIS 2005年第1期41卷 144-147页

作者： Knopov, P. S. Kasitskaya, E. I. Natl Acad Sci Ukraine Inst Cybernet Kiev Ukraine

dThis paper is devoted to the investigation of a stochastic programming problem with a convex criterion function in the case where the random factor is a stationary ergodic sequence. The problem is approximated by the problem of minimization of an empirical function. It is proved that, under some conditions, the empirical estimate coincides with the solution of the former problem in the case of a great number of observations and that the probability of large deviations of the empirical estimate from the solution of the initial problem decreases exponentially with increasing the number of observations.

关键词： stochastic programming problem empirical estimate consistency of estimates large deviations hypermixing

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Guaranteeing approach to solving quantile optimization problems

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Annals of Operations Research 1991年第1期30卷 81-93页

作者： Kibzun, A.I. Kurbakovskiy, V.Yu. Moscow Aviation Institute Russia

This paper presents a numerical method for solving quantile optimization problems, i.e. stochastic programming problems in which the quantile of the distribution of an objective function is the criterion to be optimiz... 详细信息

关键词： extremal order statistics Quantile quasigradient stochastic approximation method stochastic programming problem

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Optimal electric power‐plant planning under uncertainty of demand by means of the scenario aggregation algorithm

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Electrical Engineering in Japan 1993年第7期113卷 85-94页

作者： Nishikawa, Yoshikazu Tezuka, Tetsuo Kita, Hajime Nakano, Shinichi Kyoto University Japan Kawasaki Heavy Industries Ltd. Japan

Recently, electric power systems have faced increasing uncertainties in demand, energy price and environmental constraints in the future. In such a situation, a plan for expansion of the system capacity must be made robust against the aforementioned uncertainties. Large‐scale power plants require a long time for construction so that the decision of construction must be made under much uncertainty in the future. On the other hand, small‐scale plants require less time for construction, i.e., the decision can be made under less uncertainty in spite of their relatively higher costs. This paper is concerned with an optimal combination of the large‐scale and the small‐scale plants having the aforementioned characteristics under uncertainty of future demand. First, the demand growth in the future is described by scenarios of demand growth branching like a tree. Then the optimization problem of the system expansion is formulated into a stochastic linear‐programming problem. An optimal solution of the problem is obtained by using the scenario‐aggregation algorithm proposed by Rockafellar and Wets. The simulation results, yielded by using a parallel computation on transputers, show that there is a possibility of constructing small‐scale power plants to cope with the uncertainty even if they are more expensive than the large‐scale plants. Copyright © 1993 Wiley Periodicals, Inc., A Wiley Company

关键词： decentralized power plants economics of scale Power plant planning stochastic programming problem uncertainty of demand

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A genetic algorithm and the monte carlo method for stochastic job-shop scheduling

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International Transactions in Operational Research 2003年第6期10卷 577-596页

作者： Yoshitomi, Y. Yamaguchi, R. Kyoto Prefectural University Japan Nippon Daybreak Co Tokyo Japan

This paper proposes a method for solving stochastic job-shop scheduling problems using a hybrid of a genetic algorithm in uncertain environments and the Monte Carlo method. First, the genetic algorithm in uncertain environments is applied to stochastic job-shop scheduling problems where the processing times are treated as stochastic variables. The Roulette strategy is adopted for selecting the optimum solution having the minimum expected value for makespan. Applying crossover based on Giffler and Thompson’s algorithm results in two offspring inheriting the ancestor’s characteristics as the operation completion times averaged up to the parent’s generation. Individuals having very high frequency through all generations are selected as the good solutions. Second, the Monte Carlo method is effectively used for finding out the approximately optimum solution among these good solutions. © 2003 Wiley Periodicals, Inc.

关键词： Genetic algorithm Monte Carlo method stochastic job-shop scheduling problem stochastic programming problem Uncertain environment

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