Second-order scenario approximation and refinement in optimization under uncertainty

Edirisinghe, N. C. P.; You, Guey-Mei

doi:10.1007/bf02187644

Cited by 13 publications

(16 citation statements)

References 22 publications

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“…Subsequently, an attempt is made to determine a simplicial coverage of smaller "volume". The details of such a procedure are beyond the scope here; see Edirisinghe and You [10] for details of such an implementation. For the purposes of the experiment, an initial simplex was chosen arbitrarily.…”

Section: Computational Resultsmentioning

confidence: 98%

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Multiperiod Portfolio Optimization with Terminal Liability: Bounds for the Convex Case

Edirisinghe

2005

Comput Optim Applic

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This paper is concerned with an investor trading in multiple securities over many time periods in order to meet an outstanding liability at some future date. The investor is concerned with maximizing the expected profits from portfolio rebalancing under an initial wealth restriction to meet the future liabilities. We formulate the problem as a discrete-time stochastic optimization model and allow asset prices to have continuous probability distributions on compact domains. For the case of Markovian price uncertainty and convex terminal liability, we develop a simplicial approximation, under which bounds on the problem can be computed efficiently. Computations only require evaluating a dynamic programming recursion, which thus, allows its application to problems with a large number of trading periods. The bounds are tight in that they are exact in certain cases. Numerical results are given to demonstrate the computational efficiency of the procedure.

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Section: Computational Resultsmentioning

confidence: 98%

“…The author has developed procedures to refine the simplex as compactly as possible in order to tighten the bounds. Our future work will address the issue of computing complementary bounds, as well as procedures for refining the bounds under partitioning of the simplices, see [10] for a discussion on simplicial partitioning.…”

Section: Discussionmentioning

confidence: 99%

Multiperiod Portfolio Optimization with Terminal Liability: Bounds for the Convex Case

Edirisinghe

2005

Comput Optim Applic

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“…Moreover, v * k from (17) is identical to that of (14), and hence, from the proof of Theorem 5.1 all of the buffers at j * are drained at the same time. If l∈C j * Q l α 0 m l > 0, then k∈C j * v * k = 1 and, as earlier, (9c) holds by condition (a) of Theorem 4.1.…”

Section: Random Incoming Ratesmentioning

confidence: 90%

“…By increasing the number of cells n, we can ensure that the conditional Jensen and EM bounds, as well as the solutions v * (n), converge to their counterparts for problem (9). Development of this sequential approximation method using the Jensen and EM bounds begins with Huang, Ziemba, and Ben-Tal [21], and adaptive schemes for forming the cell-based partition of the support are described, for example, by [8,14,16,23]. Table 1 also shows the computation time required to solve instances of model (21) for n = 10, 000 i.i.d.…”

Section: Proof: It Suffices To Showmentioning

confidence: 99%

Minimizing Makespan in a Multiclass Fluid Network With Parameter Uncertainty

Büke

Hasenbein

Morton

2009

Prob. Eng. Inf. Sci.

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We introduce and investigate a new type of decision problem related to multiclass fluid networks. Optimization problems arising from fluid networks with known parameters have been studied extensively in the queueing, scheduling, and optimization literature. In this article, we explore the makespan problem in fluid networks, with the assumption that the parameters are known only through a probability distribution. Thus, the decision maker does not have complete knowledge of the parameters in advance. This problem can be formulated as a stochastic nonlinear program. We provide necessary and sufficient feasibility conditions for this class of problems. We also derive a number of other structural results that can be used in developing effective computational procedures for solving stochastic fluid makespan problems.

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“…With fairly dense scenario trees such models tend to become exponentially large as the number of stages and periods increase, and thus the computational cost to solve them also increases exponentially. Therefore, it would be imperative to either use approximation techniques such as [14], [13] and [15]. However, by exploiting the structure of the problem, decomposition techniques that render efficient solution of the problem are devised.…”

Section: Problem Settingmentioning

confidence: 99%

Computationally efficient solution algorithm for a large scale stochastic dynamic program

Saadouli

2010

Procedia Computer Science

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Stochastic dynamic programs suffer from the so called curse of dimensionality whereby the number of evaluations grows exponentially as the number of stages increases. This curse is further magnified when the stochastic variable is discretized as this adds another dimension to the number of evaluations required. As a result, it is computationally infeasible (in some cases outright impractical) to try solving these problems using an exhaustive search over all the parameters. Computational algorithms that combine decomposition techniques and simulation with reasonable assumptions on the stochastic variables can render very efficient solutions with a high degree of accuracy. This paper develops and tests such an algorithm to solve a large scale stochastic dynamic program. The algorithm's performance is tested through a simulation study of a system with the prescribed parameters determined by the algorithm. The results analyzed show that the algorithm generates very good solutions as validated by the performance indicators of the system. The solutions provide the managers of the system with insights into the complex relationships that characterize the system.

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Second-order scenario approximation and refinement in optimization under uncertainty

Cited by 13 publications

References 22 publications

Multiperiod Portfolio Optimization with Terminal Liability: Bounds for the Convex Case

Multiperiod Portfolio Optimization with Terminal Liability: Bounds for the Convex Case

Minimizing Makespan in a Multiclass Fluid Network With Parameter Uncertainty

Computationally efficient solution algorithm for a large scale stochastic dynamic program

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