Steepest Descent Algorithms for Optimization Under Unitary Matrix Constraint

Abrudan, Traian E.; Eriksson, Jan; Koivunen, Visa

doi:10.1109/tsp.2007.908999

Cited by 165 publications

(188 citation statements)

References 40 publications

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“…Assuming that the quantity of electricity generated remains consistent after the optimization in a power plant, let u be the power consumption rate of the power plant, i q as the quantity of electricity generated by each generator unit, Q as the total electricity in the grid, k as the number of generator unit in this facility and l as the number of generator unit in other facilities [6], the relation of these variables can be described as:…”

Section: The Constraint Matrix Of Independent Power Generation Optimimentioning

confidence: 99%

The Researching Mode Based on Generating Self-optimization of Global Optimization

Zou¹,

Hu²,

Zhigong³

et al. 2015

TOPEJ

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A method of global optimizing power generation is introduced in this paper. Under the condition of maintaining the same working hours of different units, electricity quantity generated between the different power suppliers is equal in one province, and it is also fulfilling the primary electricity schedule with a secure stable power system and low emission. This method is capable of minimizing resource consumption and emission while satisfying the power requirement by independently adjusting electricity generating units internally to optimum. Therefore, it is an important and effective way to promote energy saving in power generating and controlling.

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Section: The Constraint Matrix Of Independent Power Generation Optimimentioning

confidence: 99%

The Researching Mode Based on Generating Self-optimization of Global Optimization

Zou¹,

Hu²,

Zhigong³

et al. 2015

TOPEJ

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“…17. We define the tangent vector G (n) U as the derivative projected onto the tangent space of all unitaries located about U (n) ,…”

Section: Energy Minimization With Samplingmentioning

confidence: 99%

Variational Monte Carlo with the multiscale entanglement renormalization ansatz

Ferris

Vidal

2012

Phys. Rev. B

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Monte Carlo sampling techniques have been proposed as a strategy to reduce the computational cost of contractions in tensor network approaches to solving many-body systems. Here, we put forward a variational Monte Carlo approach for the multiscale entanglement renormalization ansatz (MERA), which is a unitary tensor network. Two major adjustments are required compared to previous proposals with nonunitary tensor networks. First, instead of sampling over configurations of the original lattice, made of L sites, we sample over configurations of an effective lattice, which is made of just ln(L) sites. Second, the optimization of unitary tensors must account for their unitary character while being robust to statistical noise, which we accomplish with a modified steepest descent method within the set of unitary tensors. We demonstrate the performance of the variational Monte Carlo MERA approach in the relatively simple context of a finite quantum spin chain at criticality, and discuss future, more challenging applications, including two-dimensional systems.

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“…There are several works on optimization under the orthonormality constraint. A good review is presented in [Abrudan et al, 2008], and a very important paper worth mentioning is [Edelman et al, 1998], in which a geometrical framework is presented which helps in understanding this type of problems.…”

Section: Orthonormality Constraintmentioning

confidence: 99%

“…A very convenient way of optimizing a cost function by means of gradient descent such that a matrix is orthonormal, is to use a multiplicative update and only perform rotations [Abrudan et al, 2008]. That is, the update equation is the following 17) where \bfitR (t) \in \BbbR D\times D is a rotation matrix.…”

Section: Orthonormality Constraintmentioning

confidence: 99%

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Contributions to High-Dimensional Pattern Recognition

Santamaría

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/ Resumen / ResumThis thesis gathers some contributions to statistical pattern recognition particularly targeted at problems in which the feature vectors are high-dimensional. Three pattern recognition scenarios are addressed, namely pattern classification, regression analysis and score fusion. For each of these, an algorithm for learning a statistical model is presented. In order to address the difficulty that is encountered when the feature vectors are high-dimensional, adequate models and objective functions are defined. The strategy of learning simultaneously a dimensionality reduction function and the pattern recognition model parameters is shown to be quite effective, making it possible to learn the model without discarding any discriminative information. Another topic that is addressed in the thesis is the use of tangent vectors as a way to take better advantage of the available training data. Using this idea, two popular discriminative dimensionality reduction techniques are shown to be effectively improved. For each of the algorithms proposed throughout the thesis, several data sets are used to illustrate the properties and the performance of the approaches. The empirical results show that the proposed techniques perform considerably well, and furthermore the models learned tend to be very computationally efficient.Esta tesis re\' une varias contribuciones al reconocimiento estad\' {\i} stico de formas orientadas particularmente a problemas en los que los vectores de caracter\' {\i} sticas son de una alta dimensionalidad. Tres escenarios de reconocimiento de formas se tratan, espec\' {\i} ficamente clasificaci\' on de patrones, an\' alisis de regresi\' on y fusi\' on de valores. Para cada uno de estos, un algoritmo para el aprendizaje de un modelo estad\' {\i} stico es presentado. Para poder abordar las dificultades que se encuentran cuando los vectores de caracter\' {\i} sticas son de una alta dimensionalidad, modelos y funciones objetivo adecuadas son definidas. La estrategia de aprender simult\' aneamente una funci\' on de reducci\' on de dimensionalidad y el modelo de reconocimiento se demuestra que es muy efectiva, haciendo posible aprender el modelo sin desechar nada de informaci\' on discriminatoria. Otro tema que es tratado en la tesis es el uso de vectores tangentes como una forma para aprovechar mejor los datos de entrenamiento disponibles. Usando esta idea, dos m\' etodos populares para la reducci\' on de dimensionalidad discriminativa se muestra que efectivamente mejoran. Para cada uno de los algoritmos propuestos a lo largo de la tesis, varios conjuntos de datos son usados para ilustrar las propiedades y el desempe\ño de las t\' ecnicas. Los resultados emp\' {\i} ricos muestran que las t\' ecnicas propuestas tienen un desempe\ño considerablemente bueno, y adem\' as los modelos aprendidos tienden a ser bastante eficientes computacionalmente. iv ABSTRACT / RESUMEN / RESUM Esta tesi reunix diverses contribucions al reconeixement estad\' {\i} stic de formes, les quals estan orientades ...

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Steepest Descent Algorithms for Optimization Under Unitary Matrix Constraint

Cited by 165 publications

References 40 publications

The Researching Mode Based on Generating Self-optimization of Global Optimization

The Researching Mode Based on Generating Self-optimization of Global Optimization

Variational Monte Carlo with the multiscale entanglement renormalization ansatz

Contributions to High-Dimensional Pattern Recognition

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