We propose a new method for certain multistage stochastic programs with linear or nonlinear objective function, combining a primal interior point approach with a linear-quadratic control problem over the scenario tree...
详细信息
We propose a new method for certain multistage stochastic programs with linear or nonlinear objective function, combining a primal interior point approach with a linear-quadratic control problem over the scenario tree. The latter problem, which is the direction finding problem for the barrier subproblem is solved through dynamic programming using Riccati equations. In this way we combine the low iteration count of interior point methods with an efficient solver for the subproblems. The computational results are promising, We have solved a financial problem with 1,000,000 scenarios, 15,777,740 variables and 16,888,850 constraints in 20 hours on a moderate computer. (C) 2002 Elsevier Science B.V. All rights reserved.
In [Euro. J. Operat. Res. 143 (2002) 452;Opt. Meth. Software 17 (2002) 383] a Riccati-based primal interior point method for multistage stochastic programmes was developed. This algorithm has several interesting featu...
详细信息
In [Euro. J. Operat. Res. 143 (2002) 452;Opt. Meth. Software 17 (2002) 383] a Riccati-based primal interior point method for multistage stochastic programmes was developed. This algorithm has several interesting features. It can solve problems with a nonlinear node-sepatable convex objective, local linear constraints and global linear constraints. This paper demonstrates that the algorithm can be efficiently parallelized. The solution procedure in the algorithm allows for a simple but efficient method to distribute the computations. The parallel algorithm has been implemented on a low-budget parallel computer, where we experience almost perfect linear speedup and very good scalability of the algorithm. (C) 2003 Elsevier Science B.V. All rights reserved.
Problems of multi-stage decision under uncertainty are usually classified into “stochastic” and “adaptive” ones, depending on whether the decision maker does or does not know the relevant probability distribution....
详细信息
Problems of multi-stage decision under uncertainty are usually classified into “stochastic” and “adaptive” ones, depending on whether the decision maker does or does not know the relevant probability distribution. If the Bayesian approach is taken, then, in the adaptive case, the decision maker is assumed to know the prior distribution of certain parameters. It is shown in the paper that the adaptive case is then reducible to the stochastic one.
Energy storage units offer vital balancing power for energy systems with an increasing amount of variable renewable energy (VRE) sources. The operation of such systems can be optimized by stochastic programming, which...
详细信息
Energy storage units offer vital balancing power for energy systems with an increasing amount of variable renewable energy (VRE) sources. The operation of such systems can be optimized by stochastic programming, which anticipates the uncertainty related to the variable renewable energy sources. However, these optimization problems can only be formulated for optimization horizons with a finite length, due to the rapidly increasing problem size and uncertainty in VRE production. Realistic valuation of the stored energy at the end of a horizon is important for long-term operation of the system. In this work, we investigate two different valuation methods, which are based on forecasted electricity prices, for storage-only and producer-oriented energy systems that participate in the day-ahead market. On a case study on the German day-ahead market, the methods yield competitive profits with reduced cycling of the energy storage unit and deviations with respect to the day-ahead trading.
When solving a decision problem under uncertainty via stochastic programming it is essential to choose or to build a suitable stochastic programming model taking into account the nature of the real-life problem, chara...
详细信息
When solving a decision problem under uncertainty via stochastic programming it is essential to choose or to build a suitable stochastic programming model taking into account the nature of the real-life problem, character of input data, availability of software and computer technology. Besides a brief review of history and achievements of stochastic programming, selected modeling issues concerning applications of multistage stochastic programs with recourse (the choice of the horizon, stages, methods for generating scenario trees, etc.) will be discussed. (C) 2002 Published by Elsevier Science B.V.
From the point of view of revenue management, a bi-level optimization model is proposed to determine the seat allocation and discriminatory pricing for high speed rail. The relation between ticket prices and quantitie...
详细信息
ISBN:
(数字)9780784479810
ISBN:
(纸本)9780784479810
From the point of view of revenue management, a bi-level optimization model is proposed to determine the seat allocation and discriminatory pricing for high speed rail. The relation between ticket prices and quantities can be represented using demand functions. stochastic passenger demands and demand functions of high speed rail are integrated into this model. The objective is to maximize the expected total revenue. Discriminatory pricing principles and seat capacity constraints are considered simultaneously. For different market segments, discriminative ticket prices are determined in accordance with the given seat amount. The upper-level model is formulated as a nonlinear mathematical program. The lower-level model is formulated as a two-stage stochastic programming model.
In 5G / beyond, local communication systems with small cells managed by micro operators are collecting attentions, where interference mitigation and power saving is considered as an important topic. This paper present...
详细信息
ISBN:
(纸本)9781665483032
In 5G / beyond, local communication systems with small cells managed by micro operators are collecting attentions, where interference mitigation and power saving is considered as an important topic. This paper presents an interference management method aided by spectrum database based on stochastic programming assuming non-line of sight (NLOS) environment. Regarding analysis of signal to interference plus noise ratio (SINR) under multiuser Rayleigh channel, density functions of SINR are approximated by exponential distributions. Then chance constraints in stochastic programming concerning outage SINR which are hard to deal with are converted to Monte Carlo expression for approximating predetermined outage SINR inequalities to improve the feasibility of the problem. Computer simulations show the proposed approach utilizing spectrum database is effective for performance improvement in small cellular system by micro operator.
We consider the case when part of the uncertainty faced by a decision maker is derived from actions of another independent actor who pursues her own aims. Each party sets its decisions in the next time period in respo...
详细信息
We consider the case when part of the uncertainty faced by a decision maker is derived from actions of another independent actor who pursues her own aims. Each party sets its decisions in the next time period in response to the other party's policy. We model this situation by introducing some ideas from game theory, but unlike this theory we do not focus on equilibrium and related optimality notions. Instead, we follow the framework of stochastic programming and take the view of one of the decision makers. Our model is placed in a telecommunication environment with a network owner and operators without their own network facilities. We give an extension to a multiperiod model.
In this paper we examine the biform games modeling framework. More specifically, we recast biform games as two-stage stochastic programming with recourse. The two-stage stochastic programming view of biform games is d...
详细信息
In this paper we examine the biform games modeling framework. More specifically, we recast biform games as two-stage stochastic programming with recourse. The two-stage stochastic programming view of biform games is demonstrated in this paper on an example from Brandenburger and Stuart (2007) regarding a coordination game. We claim that our stochastic programming format for biform games allows for a well established mathematical methodology to enrich the modeling options when applied to biform competitive and cooperative game options. Published by Elsevier B.V.
We study a stochastic programming approach to multicriteria multi-period portfolio optimization problem. We use a Single Index Model to estimate the returns of stocks from a market-representative index and a random wa...
详细信息
We study a stochastic programming approach to multicriteria multi-period portfolio optimization problem. We use a Single Index Model to estimate the returns of stocks from a market-representative index and a random walk model to generate scenarios on the possible values of the index return. We consider expected return, Conditional Value at Risk and liquidity as our criteria. With stocks from Istanbul Stock Exchange, we make computational studies for the two and three-criteria cases. We demonstrate the tradeoffs between criteria and show that treating these criteria simultaneously yields meaningful efficient solutions. We provide insights based on our experiments.
暂无评论