Journal of Optimization Theory and Applications, 2017
In this work, we describe the efficient use of improved directions of negative curvature for the ... more In this work, we describe the efficient use of improved directions of negative curvature for the solution of bound-constrained nonconvex problems. We follow an interior-point framework, in which the key point is the inclusion of computational low-cost procedures to improve directions of negative curvature obtained from a factorisation of the KKT matrix. From a theoretical point of view, it is well known that these directions ensure convergence to second-order KKT points. As a novelty, we consider the convergence rate of the algorithm with exploitation of negative curvature information. Finally, we test the performance of our proposal on both CUTEr/st and simulated problems, showing empirically that the enhanced directions affect positively the practical performance of the procedure.
2003 IEEE Power Engineering Society General Meeting (IEEE Cat. No.03CH37491)
This work describes a procedure that determines the optimal allocation for the yearly energy resu... more This work describes a procedure that determines the optimal allocation for the yearly energy resulting from random water inflows to the different subperiods of a year so that the expected benefits are maximized. Its main idea is to distribute the energy stored in reservoirs in each period into two parts: one is directly sold in the energy market, while the
The procedures for the identification of outlier observations that are most reliable are based on... more The procedures for the identification of outlier observations that are most reliable are based on the use of a robustified Mahalanobis distance, and have a very high computational cost even for small size problems. All these procedures present difficulties when applied to the identification of point-mass contaminations, where the outIiers are grouped into one or more clusters, separated from the sample. In this work a specific method for this contamination pattern is described, and shown to be able to handle successfully those cases where methods based on robust estimators (the Minimum Volume ElIipsiod estimator or the Stahel-Donoho estimator) fail. The method is simple, exploratory in nature, and straightforward to apply using any standard statistical software package.
In this report a new decomposition methodology for optimization problems is presented. The propos... more In this report a new decomposition methodology for optimization problems is presented. The proposed procedure is general, simple and efficient. It avoids most disadvantages of other common decomposition techniques, such as Lagrangian Relaxation or Augmented Lagrangian Relaxation. The new methodology is applied to a problem coming from interconnected power systems. The application of the new method to this problem allows the computation of an optimal coordinated but decentralized solution. Local and global convergence properties of the proposed decomposition algorithm are described. Numerical results show that the new decentralized methodology has a lower computational cost than other decomposition techniques, and in large-scale cases even lower than a centralized approach.
Although the Stahel-Donoho estimator with resampling seems to o¤er an excellent compro-mise betwe... more Although the Stahel-Donoho estimator with resampling seems to o¤er an excellent compro-mise between computational cost and bias and variability properties among high breakdown point scale estimators, it still presents signi…cantly high bias when the outliers are close to the uncontaminated sample. In this paper, we analyze di¤erent possible causes for these high values, and o¤er two pro-cedures, based on the use of alternative measures of scale for the projections de…ning the weights for the observations, that partially o¤set these undesirable e¤ects.
Studies in Classification, Data Analysis, and Knowledge Organization, 2006
ABSTRACT A projection method for robust estimation of shape and location in multivariate data and... more ABSTRACT A projection method for robust estimation of shape and location in multivariate data and cluster analysis is presented. The key idea of the procedure is to search for heterogeneity in univariate projections on directions that are obtained both randomly, using a modification of the Stahel-Donoho procedure, and by maximizing and minimizing the kurtosis coefficient of the projected data, as proposed by Peña and Prieto (2005). We show in a Monte Carlo study that the resulting procedure works well for robust estimation. Also, it preserves the good theoretical properties of the Stahel-Donoho method.
We present an e-cient implementation of an interior-point algorithm for non-convex bound constrai... more We present an e-cient implementation of an interior-point algorithm for non-convex bound constrained problems that uses good directions of negative curvature. These directions should improve the computational e-ciency of the procedure and ensure convergence to second-order KKT points. We analyze the practical behavior of the procedure and present two sets of numerical experiments to check the relevance of the algorithm.
Journal of Optimization Theory and Applications, 2017
In this work, we describe the efficient use of improved directions of negative curvature for the ... more In this work, we describe the efficient use of improved directions of negative curvature for the solution of bound-constrained nonconvex problems. We follow an interior-point framework, in which the key point is the inclusion of computational low-cost procedures to improve directions of negative curvature obtained from a factorisation of the KKT matrix. From a theoretical point of view, it is well known that these directions ensure convergence to second-order KKT points. As a novelty, we consider the convergence rate of the algorithm with exploitation of negative curvature information. Finally, we test the performance of our proposal on both CUTEr/st and simulated problems, showing empirically that the enhanced directions affect positively the practical performance of the procedure.
2003 IEEE Power Engineering Society General Meeting (IEEE Cat. No.03CH37491)
This work describes a procedure that determines the optimal allocation for the yearly energy resu... more This work describes a procedure that determines the optimal allocation for the yearly energy resulting from random water inflows to the different subperiods of a year so that the expected benefits are maximized. Its main idea is to distribute the energy stored in reservoirs in each period into two parts: one is directly sold in the energy market, while the
The procedures for the identification of outlier observations that are most reliable are based on... more The procedures for the identification of outlier observations that are most reliable are based on the use of a robustified Mahalanobis distance, and have a very high computational cost even for small size problems. All these procedures present difficulties when applied to the identification of point-mass contaminations, where the outIiers are grouped into one or more clusters, separated from the sample. In this work a specific method for this contamination pattern is described, and shown to be able to handle successfully those cases where methods based on robust estimators (the Minimum Volume ElIipsiod estimator or the Stahel-Donoho estimator) fail. The method is simple, exploratory in nature, and straightforward to apply using any standard statistical software package.
In this report a new decomposition methodology for optimization problems is presented. The propos... more In this report a new decomposition methodology for optimization problems is presented. The proposed procedure is general, simple and efficient. It avoids most disadvantages of other common decomposition techniques, such as Lagrangian Relaxation or Augmented Lagrangian Relaxation. The new methodology is applied to a problem coming from interconnected power systems. The application of the new method to this problem allows the computation of an optimal coordinated but decentralized solution. Local and global convergence properties of the proposed decomposition algorithm are described. Numerical results show that the new decentralized methodology has a lower computational cost than other decomposition techniques, and in large-scale cases even lower than a centralized approach.
Although the Stahel-Donoho estimator with resampling seems to o¤er an excellent compro-mise betwe... more Although the Stahel-Donoho estimator with resampling seems to o¤er an excellent compro-mise between computational cost and bias and variability properties among high breakdown point scale estimators, it still presents signi…cantly high bias when the outliers are close to the uncontaminated sample. In this paper, we analyze di¤erent possible causes for these high values, and o¤er two pro-cedures, based on the use of alternative measures of scale for the projections de…ning the weights for the observations, that partially o¤set these undesirable e¤ects.
Studies in Classification, Data Analysis, and Knowledge Organization, 2006
ABSTRACT A projection method for robust estimation of shape and location in multivariate data and... more ABSTRACT A projection method for robust estimation of shape and location in multivariate data and cluster analysis is presented. The key idea of the procedure is to search for heterogeneity in univariate projections on directions that are obtained both randomly, using a modification of the Stahel-Donoho procedure, and by maximizing and minimizing the kurtosis coefficient of the projected data, as proposed by Peña and Prieto (2005). We show in a Monte Carlo study that the resulting procedure works well for robust estimation. Also, it preserves the good theoretical properties of the Stahel-Donoho method.
We present an e-cient implementation of an interior-point algorithm for non-convex bound constrai... more We present an e-cient implementation of an interior-point algorithm for non-convex bound constrained problems that uses good directions of negative curvature. These directions should improve the computational e-ciency of the procedure and ensure convergence to second-order KKT points. We analyze the practical behavior of the procedure and present two sets of numerical experiments to check the relevance of the algorithm.
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