Optimization—Theory and Practice

Forst, Wilhelm; Hoffmann, Dieter

doi:10.1007/978-0-387-78977-4

Cited by 85 publications

(51 citation statements)

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“…Since the constraint inequality condition sets p i ≥ 0 is convex and the equality constraint j p j = 1 is linear, by the Karush-Kuhn-Tucker theorem [20], the following KKT condition must be satisfied while solving the above optimization problem.…”

Section: The Pauli B -Distance Of Qubit Statementioning

confidence: 99%

Complete optimal convex approximations of qubit states under $$B_2$$ B 2 distance

Liang¹,

Li²,

Ye³

et al. 2018

Quantum Inf Process

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We consider the optimal approximation of arbitrary qubit states with respect to an available states consisting the eigenstates of two of three Pauli matrices, the B 2 -distance of an arbitrary target state. Both the analytical formulae of the B 2 -distance and the corresponding complete optimal decompositions are obtained. The tradeoff relations for both the sum and the squared sum of the B 2 -distances have been analytically and numerically investigated.

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Section: The Pauli B -Distance Of Qubit Statementioning

confidence: 99%

Complete optimal convex approximations of qubit states under $$B_2$$ B 2 distance

Liang¹,

Li²,

Ye³

et al. 2018

Quantum Inf Process

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“…QN is one of the most efficient gradient-based optimization algorithms [10,11] and commonly-used training method for highly nonlinear function problems [2][3][4][5][6]. Note that, the secant equation,…”

Section: Quasi-newton Algorithmmentioning

confidence: 99%

A novel quasi-Newton-based optimization for neural network training incorporating Nesterov's accelerated gradient

Ninomiya

2017

NOLTA

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This paper describes a novel quasi-Newton (QN) based accelerated technique for training of neural networks. Recently, Nesterov's accelerated gradient method has been utilized for the acceleration of the gradient-based training. In this paper the acceleration of the QN training algorithm is realized by the quadratic approximation of the error function incorporating the momentum term as Nesterov's method. It is shown that the proposed algorithm has a similar convergence property with the QN method. Neural network trainings for the function approximation and the microwave circuit modeling problems are presented to demonstrate the proposed algorithm. The method proposed here drastically improves the convergence speed of the conventional QN algorithm.

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“…The interior-point method [17] is used to optimize parameter values by minimizing the Mean Square Error (MSE) between the final model and windows of the AIR. At the beginning of the process we setD = 0,β = ∅ andk = ∅.…”

Section: Model Parameter Fittingmentioning

confidence: 99%

Sparse parametric modeling of the early part of acoustic impulse responses

Papayiannis

Evers

Naylor

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Acoustic channels are typically described by their Acoustic Impulse Response (AIR) as a Moving Average (MA) process. Such AIRs are often considered in terms of their early and late parts, describing discrete reflections and the diffuse reverberation tail respectively. We propose an approach for constructing a sparse parametric model for the early part. The model aims at reducing the number of parameters needed to represent it and subsequently reconstruct from the representation the MA coefficients that describe it. It consists of a representation of the reflections arriving at the receiver as delayed copies of an excitation signal. The Time-Of-Arrivals of reflections are not restricted to integer sample instances and a dynamically estimated model for the excitation sound is used. We also present a corresponding parameter estimation method, which is based on regularized-regression and nonlinear optimization. The proposed method also serves as an analysis tool, since estimated parameters can be used for the estimation of room geometry, the mixing time and other channel properties. Experiments involving simulated and measured AIRs are presented, in which the AIR coefficient reconstruction-error energy does not exceed 11.4% of the energy of the original AIR coefficients. The results also indicate dimensionality reduction figures exceeding 90% when compared to a MA process representation.

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Optimization—Theory and Practice

Cited by 85 publications

References 0 publications

Complete optimal convex approximations of qubit states under $$B_2$$ B 2 distance

Complete optimal convex approximations of qubit states under $$B_2$$ B 2 distance

A novel quasi-Newton-based optimization for neural network training incorporating Nesterov's accelerated gradient

Sparse parametric modeling of the early part of acoustic impulse responses

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