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An interior point approach to postoptimal . . .
 JOURNAL OF OPERATIONS RESEARCH
, 1993
"... In practice, understanding the behavior of the solution of the linear programming problem due to changes in the data is often as important as obtaining the optimal solution itself. Postoptimal analysis based on the simplex method by using an optimal basis is well established and widely used. However ..."
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Cited by 16 (6 self)
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In practice, understanding the behavior of the solution of the linear programming problem due to changes in the data is often as important as obtaining the optimal solution itself. Postoptimal analysis based on the simplex method by using an optimal basis is well established and widely used. However, in case of degenerate optimal solutions, due to nonunicity of optimal bases, problems arise in correct interpretation of the results of the analysis; partial, in a certain sense erroneous, information is e.g. provided by commercial packages for linear programming. We discuss the problems in this approach and the proposals that have been made to resolve the difficulties. Then we investigate postoptimal analysis in linear programming from an interior point of view. We make use of the partition of the variables induced by a pair of strictly complementary solutions (the optimal partition), which is uniquely determined and arises as a natural concept in interior point methods. We give example...
Optimal Sequential Exploration: Bandits, Clairvoyants, and Wildcats. submitted, accessible at http://faculty.fuqua.duke.edu/ jes9/bio/OptimalSequentialExplorationBCW.pdf
, 2012
"... This paper was motivated by the problem of developing an optimal strategy for exploring a large oil and gas field in the North Sea. Where should we drill first? Where do we drill next? The problem resembles a classical multiarmed bandit problem, but probabilistic dependence plays a key role: outcome ..."
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Cited by 4 (0 self)
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This paper was motivated by the problem of developing an optimal strategy for exploring a large oil and gas field in the North Sea. Where should we drill first? Where do we drill next? The problem resembles a classical multiarmed bandit problem, but probabilistic dependence plays a key role: outcomes at drilled sites reveal information about neighboring targets. Good exploration strategies will take advantage of this information as it is revealed. We develop heuristic policies for sequential exploration problems and complement these heuristics with upper bounds on the performance of an optimal policy. We begin by grouping the targets into clusters of manageable size. The heuristics are derived from a model that treats these clusters as independent. The upper bounds are given by assuming each cluster has perfect information about the results from all other clusters. The analysis relies heavily on results for bandit superprocesses, a generalization of the classical multiarmed bandit problem. We evaluate the heuristics and bounds using Monte Carlo simulation and, in our problem, we find that the heuristic policies are nearly optimal.