Quadratic programming with one negative eigenvalue is NP-hard

Pardalos, Pãnos M.; Vavasis, Stephen A.

doi:10.1007/bf00120662

Cited by 403 publications

(221 citation statements)

References 8 publications

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“…This has been a popular approach in the practice and literature see (Jorion, 2003). However, this would create a non-linearity in the objective as the variance of the difference of the returns of the tracking and benchmark portfolios would need to be minimized and in conjunction with cardinality constraint requirements would result in a quadratic non-linear integer program which is known to be very challenging to solve see (Bertsimas and Shioda, 2009;Pardalos and Vavasis, 1991).…”

Section: Basic Cluster-based Index Tracking Modelmentioning

confidence: 99%

A constrained cluster-based approach for tracking the S&P 500 index

Kwon

Costa

2017

International Journal of Production Economics

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A B S T R A C TWe consider the problem of tracking a benchmark target portfolio of financial securities in particular the S&P 500. Linear integer programming models are developed that seeks to track a target portfolio using a strict subset of securities from the benchmark portfolio. The models represent a clustering approach to select securities and also include additional constraints that aim to control risk and transactions costs. Lagrangian and semi-Lagrangian methods are developed to compute solutions to the tracking models. The computational results show the effectiveness of the linear tracking models and the computational methods in tracking the S&P 500. Overall, the models and methods presented can serve as the basis of the optimization module in an optimization-based decision support for creating tracking portfolios.

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Section: Basic Cluster-based Index Tracking Modelmentioning

confidence: 99%

A constrained cluster-based approach for tracking the S&P 500 index

Kwon

Costa

2017

International Journal of Production Economics

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“…The maximization of x T Wx under the given constraints is known to be NP-hard, if W has positive eigenvalues (Gibbons et al, 1997;Pardalos and Vavasis, 1991). This is the case in our application as W is not guaranteed to be negative semi-definite.…”

Section: Replicator Dynamicsmentioning

confidence: 99%

The parcellation of cortical areas using replicator dynamics in fMRI

et al. 2006

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“…In this case, matrix is an indefinite matrix: therefore, optimization problem (13) is a non-convex optimization problem. Such kind of problems is NP-hard [37]. There are algorithms for obtaining the global optimum of non convex quadratic optimization problems, such as the LPCC method [38] and the globally solving method based on completely positive programming [39].…”

Section: Optimizationmentioning

confidence: 99%

Optimization of the electrochemical impedance spectroscopy measurement parameters for PEM fuel cell spectrum determination

Giner-Sanz

Ortega

Pérez-Herranz

2015

Electrochimica Acta

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ElsevierGiner Sanz, JJ.; Ortega Navarro, EM.; Pérez-Herranz, V. (2015). Optimization of the electrochemical impedance spectroscopy measurement parameters for PEM fuel cell spectrum determination. Electrochimica Acta. 174:1290Acta. 174: -1298Acta. 174: . doi:10.1016Acta. 174: /j.electacta.2015 Optimization of the electrochemical impedance spectroscopy measurement parameters for PEM fuel cell spectrum determination Keywords: Electrochemical Impedance Spectroscopy; measurement parameters; optimization; factorial experimental design; PEMFC. AbstractCurrently, electrochemical Impedance Spectroscopy (EIS) is a widely used tool for the study of electrochemical systems, in general; and fuel cells, in particular. A great effort is typically invested in the analysis of the obtained spectra; whereas, little time is usually spent optimizing the measurement parameters used to obtain these spectra. In general, the default settings provided by the control software used to perform the measurements, or the parameters used in similar systems available in literature, are selected to carry out the measurements. The goal of this work is to determine the optimal measurement parameters for obtaining impedance spectra of a commercial PEM fuel cell. In order to achieve this, a 2 5 factorial design was considered. Five factors were considered, the five impedance spectroscopy measurement parameters: maximum integration time; minimum number of integration cycles; number of stabilization cycles; maximum stabilization time; and minimum cycle fraction. For each factor combination envisaged in the experimental design, the cell spectrum was obtained in given operation conditions, for which the reference spectrum of the system was known, since it had been determined in previous works. The experimentally obtained spectra were fitted to the reference electric equivalent circuit. The mean square error between the experimental data fitting and the reference spectrum fitting was determined in each case, and was used as the dependant variable for the experimental design analysis. An analysis of the variance was performed in order to determine which measurement parameters have a significant effect on the dependant variable; and a model relating the dependant variable and the measurement parameters was built. This model was used in order to obtain the optimal value of each one of the measurement parameters that minimized the mean square error of the fit obtained from the experimental data with respect to the reference fit.

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Quadratic programming with one negative eigenvalue is NP-hard

Cited by 403 publications

References 8 publications

A constrained cluster-based approach for tracking the S&P 500 index

A constrained cluster-based approach for tracking the S&P 500 index

The parcellation of cortical areas using replicator dynamics in fMRI

Optimization of the electrochemical impedance spectroscopy measurement parameters for PEM fuel cell spectrum determination

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