On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems

Lai, Kin Keung; Mishra, Shashi Kant; Ram, Bhagwat

doi:10.3390/math8040616

Cited by 18 publications

(21 citation statements)

References 45 publications

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“…under boundary conditions k(0) = k (0) = 0 and k ( 3 8 ) = 15 4 k (1) for t ∈ (0, 1) such that the assumptions of Lemma 3.6 hold. Clearly, σ = 18 7 ∈ (2, 3), ζ = 5 6 ∈ (0, 1), r = 3 8 ∈ (0, 1), and λ = 15 4 > 0. Also, λ(σ -2) = 15 7 > 1.…”

Section: Discussionmentioning

confidence: 99%

“…Soon afterward, it is further promoted by Al-Salam and Agarwal [9,10], where many outstanding theoretical results are given. Its emergence and development extended the application of interdisciplinary to be further and aroused widespread attention of the scholars; see [11][12][13][14][15][16][17][18][19][20][21][22][23] Then Liang and Zhang [24] studied the existence and uniqueness of positive solutions by properties of the Green function, the lower and upper solution method, and the fixed point theorem for the fractional equation D σ q [k](s) + w(s, k(s)) = 0 for 0 < s < 1 under the boundary conditions k(0) = k (0) = 0 and k (1) = m-2 i=1 i k (ς i ), where 2 < σ ≤ 3, and c D σ q is the Riemann-Liouville fractional derivative. In 2015, Zhang et al [25] through the spectral analysis and fixed point index theorem obtained the existence of positive solutions of the singular nonlinear fractional differential equation…”

Section: Introductionmentioning

confidence: 99%

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The existence of nonnegative solutions for a nonlinear fractional q-differential problem via a different numerical approach

et al. 2021

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This paper deals with the existence of nonnegative solutions for a class of boundary value problems of fractional q-differential equation ${}^{c}\mathcal{D}_{q}^{\sigma }[k](t) = w (t, k(t), {}^{c} \mathcal{D}_{q}^{\zeta }[k](t) )$ D q σ c [ k ] ( t ) = w ( t , k ( t ) , c D q ζ [ k ] ( t ) ) with three-point conditions for $t \in (0,1)$ t ∈ ( 0 , 1 ) on a time scale $\mathbb{T}_{t_{0}}= \{ t : t =t_{0}q^{n}\}\cup \{0\}$ T t 0 = { t : t = t 0 q n } ∪ { 0 } , where $n\in \mathbb{N}$ n ∈ N , $t_{0} \in \mathbb{R}$ t 0 ∈ R , and $0< q<1$ 0 < q < 1 , based on the Leray–Schauder nonlinear alternative and Guo–Krasnoselskii theorem. Moreover, we discuss the existence of nonnegative solutions. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The existence of nonnegative solutions for a nonlinear fractional q-differential problem via a different numerical approach

et al. 2021

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“…This provides the avenue for error minimization between the predicted and actual outputs. To achieve this cost minimization, several weight optimization algorithms exist including the quasi-Newton methods [39], Adam [40], stochastic gradient descent (SGD) [41,42]; and the popular SGD improvement-the Adam [40] weight optimizer. While the SGD serves fairly for most problems and the quasi-Newton methods are popularly efficient on small datasets, the Adam optimizer comes with faster convergence, faster learning, and improved validation accuracy for large datasets.…”

Section: Ml/dl-based Diagnosismentioning

confidence: 99%

A Wavelet-Based Diagnostic Framework for CRD Engine Injection Systems under Emulsified Fuel Conditions

Akpudo

Hur

2021

Electronics

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The impact of the constituent oxides of nitrogen, carbon, sulphur, and other particulate matter which make up the gas emissions from diesel engines has motivated several control techniques for these pollutants. Water-in-diesel emulsions provide a reliable solution, but the wear effects on the fuel injection system (FIS) still pose remarkable concerns. Because pressure signals from the common rail (CR) reflect the dynamics associated with varying emulsion compositions and at varying engine RPMs, an investigative (and diagnostic) study was conducted on a KIA Sorento 2004 four-cylinder line engine at various water-in-diesel emulsion compositions and engine speeds. Alongside visual/microscopic inspections and spectral analyses, the diagnostic framework proposed herein functions on the use of standardized first-order differentials of the CR pressure signals to generate reliable continuous wavelet coefficients (CWCs) which capture discriminative spectral and transient information for accurate diagnosis. The results show that by extracting the CWCs from the first-order CR pressure differentials up to the 512th scale on a Mexican hat wavelet, adequate fault parameters can be extracted for use by a deep neural network (DNN) whose hyperparameters were globally optimized following a grid search. With a test accuracy of 92.3% against other widely-used ML-based diagnostic tools, the proposed DNN-based diagnostics tool was empirically assessed using several performance evaluation metrics.

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“…Jackson [10,11] was the first to have some applications of the q-calculus and introduced the q-analogue of the classical derivative and integral operators. Applications of q-calculus play an important role in various fields of mathematics and physics [12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

et al. 2021

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A Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q-variant of the PRP (q-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter q approaches 1.

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On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems

Cited by 18 publications

References 45 publications

The existence of nonnegative solutions for a nonlinear fractional q-differential problem via a different numerical approach

The existence of nonnegative solutions for a nonlinear fractional q-differential problem via a different numerical approach

A Wavelet-Based Diagnostic Framework for CRD Engine Injection Systems under Emulsified Fuel Conditions

A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

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