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Numerical Optimization: Theoretical and Practical Aspects

J. Frédéric Bonnans J. Charles Gilbert Claude Lemaréchal Claudia A. Sagastizábal

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2006 SpringerLink

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Tipo de recurso:

libros

ISBN impreso

978-3-540-35445-1

ISBN electrónico

978-3-540-35447-5

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer 2006

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Tabla de contenidos

Applications of Nonsmooth Optimization

J. Frédéric Bonnans; J. Charles Gilbert; Claude Lemaréchal; Claudia A. Sagastizábal

Current predictive models in the intensive care rely on summaries of data collected at patient admission. It has been shown recently that temporal patterns of the daily Sequential Organ Failure Assessment (SOFA) scores can improve predictions. However, the derangement of the six individual organ systems underlying the calculation of a SOFA score were not taken into account, thus impeding the understanding of their prognostic merits. In this paper we propose a method for model induction that integrates in a novel way the individual organ failure scores with SOFA scores. The integration of these two correlated components is achieved by summarizing the historic SOFA information and at the same time by capturing the evolution of individual organ system failure status. The method also explicitly avoids the collinearity problem among organ failure episodes. We report on the application of our method to a large dataset and demonstrate its added value. The ubiquity of severity scores and sub-scores in medicine renders our approach relevant to a wide range of medical domains.

Part II - Nonsmooth Optimization | Pp. 161-182

Computational Exercises

J. Frédéric Bonnans; J. Charles Gilbert; Claude Lemaréchal; Claudia A. Sagastizábal

Current predictive models in the intensive care rely on summaries of data collected at patient admission. It has been shown recently that temporal patterns of the daily Sequential Organ Failure Assessment (SOFA) scores can improve predictions. However, the derangement of the six individual organ systems underlying the calculation of a SOFA score were not taken into account, thus impeding the understanding of their prognostic merits. In this paper we propose a method for model induction that integrates in a novel way the individual organ failure scores with SOFA scores. The integration of these two correlated components is achieved by summarizing the historic SOFA information and at the same time by capturing the evolution of individual organ system failure status. The method also explicitly avoids the collinearity problem among organ failure episodes. We report on the application of our method to a large dataset and demonstrate its added value. The ubiquity of severity scores and sub-scores in medicine renders our approach relevant to a wide range of medical domains.

Part II - Nonsmooth Optimization | Pp. 183-188

Background

J. Frédéric Bonnans; J. Charles Gilbert; Claude Lemaréchal; Claudia A. Sagastizábal

Current predictive models in the intensive care rely on summaries of data collected at patient admission. It has been shown recently that temporal patterns of the daily Sequential Organ Failure Assessment (SOFA) scores can improve predictions. However, the derangement of the six individual organ systems underlying the calculation of a SOFA score were not taken into account, thus impeding the understanding of their prognostic merits. In this paper we propose a method for model induction that integrates in a novel way the individual organ failure scores with SOFA scores. The integration of these two correlated components is achieved by summarizing the historic SOFA information and at the same time by capturing the evolution of individual organ system failure status. The method also explicitly avoids the collinearity problem among organ failure episodes. We report on the application of our method to a large dataset and demonstrate its added value. The ubiquity of severity scores and sub-scores in medicine renders our approach relevant to a wide range of medical domains.

Part III - Newton's Methods in Constrained Optimization | Pp. 197-214

Local Methods for Problems with Equality Constraints

J. Frédéric Bonnans; J. Charles Gilbert; Claude Lemaréchal; Claudia A. Sagastizábal

Current predictive models in the intensive care rely on summaries of data collected at patient admission. It has been shown recently that temporal patterns of the daily Sequential Organ Failure Assessment (SOFA) scores can improve predictions. However, the derangement of the six individual organ systems underlying the calculation of a SOFA score were not taken into account, thus impeding the understanding of their prognostic merits. In this paper we propose a method for model induction that integrates in a novel way the individual organ failure scores with SOFA scores. The integration of these two correlated components is achieved by summarizing the historic SOFA information and at the same time by capturing the evolution of individual organ system failure status. The method also explicitly avoids the collinearity problem among organ failure episodes. We report on the application of our method to a large dataset and demonstrate its added value. The ubiquity of severity scores and sub-scores in medicine renders our approach relevant to a wide range of medical domains.

Part III - Newton's Methods in Constrained Optimization | Pp. 215-253

Local Methods for Problems with Equality and InequalityConstraints

J. Frédéric Bonnans; J. Charles Gilbert; Claude Lemaréchal; Claudia A. Sagastizábal

Current predictive models in the intensive care rely on summaries of data collected at patient admission. It has been shown recently that temporal patterns of the daily Sequential Organ Failure Assessment (SOFA) scores can improve predictions. However, the derangement of the six individual organ systems underlying the calculation of a SOFA score were not taken into account, thus impeding the understanding of their prognostic merits. In this paper we propose a method for model induction that integrates in a novel way the individual organ failure scores with SOFA scores. The integration of these two correlated components is achieved by summarizing the historic SOFA information and at the same time by capturing the evolution of individual organ system failure status. The method also explicitly avoids the collinearity problem among organ failure episodes. We report on the application of our method to a large dataset and demonstrate its added value. The ubiquity of severity scores and sub-scores in medicine renders our approach relevant to a wide range of medical domains.

Part III - Newton's Methods in Constrained Optimization | Pp. 255-270

Exact Penalization

J. Frédéric Bonnans; J. Charles Gilbert; Claude Lemaréchal; Claudia A. Sagastizábal

Current predictive models in the intensive care rely on summaries of data collected at patient admission. It has been shown recently that temporal patterns of the daily Sequential Organ Failure Assessment (SOFA) scores can improve predictions. However, the derangement of the six individual organ systems underlying the calculation of a SOFA score were not taken into account, thus impeding the understanding of their prognostic merits. In this paper we propose a method for model induction that integrates in a novel way the individual organ failure scores with SOFA scores. The integration of these two correlated components is achieved by summarizing the historic SOFA information and at the same time by capturing the evolution of individual organ system failure status. The method also explicitly avoids the collinearity problem among organ failure episodes. We report on the application of our method to a large dataset and demonstrate its added value. The ubiquity of severity scores and sub-scores in medicine renders our approach relevant to a wide range of medical domains.

Part III - Newton's Methods in Constrained Optimization | Pp. 271-287

Globalization by Line-Search

J. Frédéric Bonnans; J. Charles Gilbert; Claude Lemaréchal; Claudia A. Sagastizábal

Current predictive models in the intensive care rely on summaries of data collected at patient admission. It has been shown recently that temporal patterns of the daily Sequential Organ Failure Assessment (SOFA) scores can improve predictions. However, the derangement of the six individual organ systems underlying the calculation of a SOFA score were not taken into account, thus impeding the understanding of their prognostic merits. In this paper we propose a method for model induction that integrates in a novel way the individual organ failure scores with SOFA scores. The integration of these two correlated components is achieved by summarizing the historic SOFA information and at the same time by capturing the evolution of individual organ system failure status. The method also explicitly avoids the collinearity problem among organ failure episodes. We report on the application of our method to a large dataset and demonstrate its added value. The ubiquity of severity scores and sub-scores in medicine renders our approach relevant to a wide range of medical domains.

Part III - Newton's Methods in Constrained Optimization | Pp. 289-322

Quasi-Newton Versions

J. Frédéric Bonnans; J. Charles Gilbert; Claude Lemaréchal; Claudia A. Sagastizábal

Current predictive models in the intensive care rely on summaries of data collected at patient admission. It has been shown recently that temporal patterns of the daily Sequential Organ Failure Assessment (SOFA) scores can improve predictions. However, the derangement of the six individual organ systems underlying the calculation of a SOFA score were not taken into account, thus impeding the understanding of their prognostic merits. In this paper we propose a method for model induction that integrates in a novel way the individual organ failure scores with SOFA scores. The integration of these two correlated components is achieved by summarizing the historic SOFA information and at the same time by capturing the evolution of individual organ system failure status. The method also explicitly avoids the collinearity problem among organ failure episodes. We report on the application of our method to a large dataset and demonstrate its added value. The ubiquity of severity scores and sub-scores in medicine renders our approach relevant to a wide range of medical domains.

Part III - Newton's Methods in Constrained Optimization | Pp. 323-344

Linearly Constrained Optimization and SimplexAlgorithm

J. Frédéric Bonnans; J. Charles Gilbert; Claude Lemaréchal; Claudia A. Sagastizábal

Current predictive models in the intensive care rely on summaries of data collected at patient admission. It has been shown recently that temporal patterns of the daily Sequential Organ Failure Assessment (SOFA) scores can improve predictions. However, the derangement of the six individual organ systems underlying the calculation of a SOFA score were not taken into account, thus impeding the understanding of their prognostic merits. In this paper we propose a method for model induction that integrates in a novel way the individual organ failure scores with SOFA scores. The integration of these two correlated components is achieved by summarizing the historic SOFA information and at the same time by capturing the evolution of individual organ system failure status. The method also explicitly avoids the collinearity problem among organ failure episodes. We report on the application of our method to a large dataset and demonstrate its added value. The ubiquity of severity scores and sub-scores in medicine renders our approach relevant to a wide range of medical domains.

Part IV - Interior-Point Algorithms for Linear and QuadraticOptimization | Pp. 353-369

Linear Monotone Complementarity and Associated Vector Fields

J. Frédéric Bonnans; J. Charles Gilbert; Claude Lemaréchal; Claudia A. Sagastizábal

Current predictive models in the intensive care rely on summaries of data collected at patient admission. It has been shown recently that temporal patterns of the daily Sequential Organ Failure Assessment (SOFA) scores can improve predictions. However, the derangement of the six individual organ systems underlying the calculation of a SOFA score were not taken into account, thus impeding the understanding of their prognostic merits. In this paper we propose a method for model induction that integrates in a novel way the individual organ failure scores with SOFA scores. The integration of these two correlated components is achieved by summarizing the historic SOFA information and at the same time by capturing the evolution of individual organ system failure status. The method also explicitly avoids the collinearity problem among organ failure episodes. We report on the application of our method to a large dataset and demonstrate its added value. The ubiquity of severity scores and sub-scores in medicine renders our approach relevant to a wide range of medical domains.

Part IV - Interior-Point Algorithms for Linear and QuadraticOptimization | Pp. 371-394