In this work, the well control optimization of the Olympus challenge is solved by two non-intrusive strategies that use the simulator as a black box. This reservoir model contains uncertainties on geological scenarios...
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In this work, the well control optimization of the Olympus challenge is solved by two non-intrusive strategies that use the simulator as a black box. This reservoir model contains uncertainties on geological scenarios, in which the optimal management process is conducted through robust optimization, which can use a set of representative realizations to honor the statistics of the geological properties. The statistic considered here is the mean of the net present value (NPV). Control variables are flow rates and bottom hole pressures (BHP) of each well completion. The first strategy used here is the sequential approximate optimization (SAO) with variable reparameterization that uses polynomial control trajectories. In order to reduce the computational cost of the overall process, this strategy builds surrogate models to be used in the several function calls required in the optimization process. The other strategy is the refined ensemble-based (REB) method that computes the approximate gradient of the expected NPV as a sum of the columns of a refined sensitivity matrix obtained from ensemble-based covariance matrices of controls and cross-covariance between well NPVs and controls. The use of small-sized ensembles introduces spurious correlations that degrade gradient quality. Non-distance-based localization and competitiveness coefficients between producer wells and smoothing control trajectories are used to reduce spurious correlations. Both strategies use approximate derivatives and they are able to include any general nonlinear constraints. The SQP (sequential quadratic programming) is the algorithm used in both methodologies. The strategies produced similar results, are close to the reactive control solution, and are viable alternatives for robust optimization problem and the choice depends mostly on the number of control variables.
Rare class problems are common in real-world applications across a wide range of domains. Standard classification algorithms are known to perform poorly in these cases, since they focus on overall classification accur...
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Rare class problems are common in real-world applications across a wide range of domains. Standard classification algorithms are known to perform poorly in these cases, since they focus on overall classification accuracy. In addition, we have seen a significant increase of data in recent years, resulting in many largescale rare class problems. In this paper, we focus on nonlinear kernel based classification methods expressed as a regularized loss minimization problem. We address the challenges associated with both rare class problems and largescale learning, by 1) optimizing area under curve of the receiver of operator characteristic in the training process, instead of classification accuracy and 2) using a rare class kernel representation to achieve an efficient time and space algorithm. We call the algorithm RankRC. We provide justifications for the rare class representation and experimentally illustrate the effectiveness of RankRC in test performance, computational complexity, and model robustness.
We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = YY(T), where the number of columns ...
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We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = YY(T), where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = YY(T) leads to a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second-order optimization method with guaranteed quadratic convergence. It furthermore provides some conditions on the rank of the factorization to ensure equivalence with the original problem. In contrast to existing methods, the proposed algorithm converges monotonically to the sought solution. Its numerical efficiency is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis.
The minimization of linear functionals defined on the solutions of discrete ill-posed problems arises, e.g., in the computation of confidence intervals for these solutions. In 1990, Elden proposed an algorithm for thi...
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The minimization of linear functionals defined on the solutions of discrete ill-posed problems arises, e.g., in the computation of confidence intervals for these solutions. In 1990, Elden proposed an algorithm for this minimization problem based on a parametric programming reformulation involving the solution of a sequence of trust-region problems, and using matrix factorizations. In this paper, we describe MLFIP, a large-scale version of this algorithm where a limited-memory trust-region solver is used on the subproblems. We illustrate the use of our algorithm in connection with an inverse heat conduction problem.
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