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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

Predictor-Corrector Algorithms

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. 395-409

Non-Feasible Algorithms

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. 411-423

Self-Duality

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. 425-434

One-Step 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 IV - Interior-Point Algorithms for Linear and QuadraticOptimization | Pp. 435-450

Complexity of Linear Optimization Problems with Integer Data

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. 451-456

Karmarkar's Algorithm

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. 457-463