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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

Cobertura temática

Tabla de contenidos

General Introduction

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 I - Unconstrained Problems | Pp. 1-20

Basic Methods

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 I - Unconstrained Problems | Pp. 25-35

Line-Searches

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 I - Unconstrained Problems | Pp. 37-50

Newtonian Methods

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 I - Unconstrained Problems | Pp. 51-66

Conjugate Gradient

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 I - Unconstrained Problems | Pp. 67-76

Special Methods

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 I - Unconstrained Problems | Pp. 77-96

A Case Study: Seismic Reection Tomography

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 I - Unconstrained Problems | Pp. 97-104

Introduction to 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. 109-118

Some Methods in 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. 119-136

Bundle Methods. The Quest for Descent

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. 137-159