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Parallel approximation to high multiplicity scheduling problems V I A smooth multi-valued quadratic programming

Maria Serna, Fatos Xhafa (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We consider the parallel approximability of two problems arising from high multiplicity scheduling, namely the unweighted model with variable processing requirements and the weighted model with identical processing requirements. These two problems are known to be modelled by a class of quadratic programs that are efficiently solvable in polynomial time. On the parallel setting, both problems are P-complete and hence cannot be efficiently solved in parallel unless P = NC. To deal with the parallel...

Parallel approximation to high multiplicity scheduling problems VIA smooth multi-valued quadratic programming

Maria Serna, Fatos Xhafa (2007)

RAIRO - Theoretical Informatics and Applications

We consider the parallel approximability of two problems arising from high multiplicity scheduling, namely the unweighted model with variable processing requirements and the weighted model with identical processing requirements. These two problems are known to be modelled by a class of quadratic programs that are efficiently solvable in polynomial time. On the parallel setting, both problems are P-complete and hence cannot be efficiently solved in parallel unless P = NC. To deal with the parallel...

POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems

Martin Kahlbacher, Stefan Volkwein (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

An optimal control problem governed by a bilinear elliptic equation is considered. This problem is solved by the sequential quadratic programming (SQP) method in an infinite-dimensional framework. In each level of this iterative method the solution of linear-quadratic subproblem is computed by a Galerkin projection using proper orthogonal decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is determined. Based on a POD a-posteriori error estimator developed by Tröltzsch...

POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems∗

Martin Kahlbacher, Stefan Volkwein (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

An optimal control problem governed by a bilinear elliptic equation is considered. This problem is solved by the sequential quadratic programming (SQP) method in an infinite-dimensional framework. In each level of this iterative method the solution of linear-quadratic subproblem is computed by a Galerkin projection using proper orthogonal decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is determined. Based on a POD...

Problema de asignación cuadrática multiobjetivo.

Angel Felipe Ortega (1989)

Trabajos de Investigación Operativa

Se define la versión multiobjetivo del Problema de Asignación Cuadrática. Se muestran los inconvenientes de la técnica de ponderación de objetivos y se desarrollan algoritmos locales bajo las metodologías de soluciones eficientes, lexicográficas y equilibradas mediante la generalización de los procedimientos r-óptimos al caso multidimensional. Se recogen resultados computacionales sobre los algoritmos propuestos.

Producing the tangency portfolio as a corner portfolio

Reza Keykhaei, Mohamad-Taghi Jahandideh (2013)

RAIRO - Operations Research - Recherche Opérationnelle

One-fund theorem states that an efficient portfolio in a Mean-Variance (M-V) portfolio selection problem for a set of some risky assets and a riskless asset can be represented by a combination of a unique risky fund (tangency portfolio) and the riskless asset. In this paper, we introduce a method for which the tangency portfolio can be produced as a corner portfolio. So, the tangency portfolio can be computed easily and fast by any algorithm designed for tracing out the M-V efficient frontier via...

Proper orthogonal decomposition for optimality systems

Karl Kunisch, Stefan Volkwein (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

Proper orthogonal decomposition (POD) is a powerful technique for model reduction of non-linear systems. It is based on a Galerkin type discretization with basis elements created from the dynamical system itself. In the context of optimal control this approach may suffer from the fact that the basis elements are computed from a reference trajectory containing features which are quite different from those of the optimally controlled trajectory. A method is proposed which avoids this problem of unmodelled...

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