Conjugate Gradient Methods for Computing Weighted Analytic Center for Linear Matrix Inequalities Using Exact and Quadratic Interpolation Line Searches

Jibrin, Shafiu; Abdullahi, Ibrahim

doi:10.11648/j.ajam.20200801.11

Cited by 3 publications

(1 citation statement)

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“…HPRP is a modification of the classical PRP method [20]. Both ZA and HPRP are implemented using the Newton's exact line search and Quadratic interpolation inexact line search [14,5]. The performance of each method on random test problems will be evaluated by observing the number of iterations and time required to find the weighted analytic center.…”

Section: Introductionmentioning

confidence: 99%

A Weighted Analytic Center for Second-Order Cone Constraints

Dawuda¹,

Jibrin²,

Abdullahi³

2021

ACM

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This paper introduces a weighted analytic center for a system of second order cone constraints. The associated barrier function is shown to be convex and conjugate gradient (CG) methods are used to compute the weighted analytic center. In contrast with Newton's-like methods, CG methods use only the gradient and not the Hessian to minimize a function. The methods considered are the HPRP and ZA with exact and inexact line searches. The exact line search uses Newton's method and quadratic interpolation is used for the inexact line search. The performance of each method on random test problems was evaluated by observing the number of iterations and time required to find the weighted analytic center. Our numerical methods indicate that ZA is better than HPRP with any of the two line searches, in terms of the number of iterations and time to find the weighted analytic center. Quadratic interpolation inexact line search gives the best success rate and fewest number of iterations for the CG methods considered. On the other hand, the fastest time for the CG methods is found with the Newton's exact line search. In addition, these results indicate that for each of the methods, our Quadratic interpolation inexact line search has a higher cost per iteration than that of the Newton's exact line search.

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Section: Introductionmentioning

confidence: 99%

A Weighted Analytic Center for Second-Order Cone Constraints

Dawuda¹,

Jibrin²,

Abdullahi³

2021

ACM

Self Cite

View full text Add to dashboard Cite

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Extracting Hidden Crime Patterns by Analysing Crime Dataset

Ibrahim,

Jain,

Bhardwaj

et al. 2024

Lecture Notes in Networks and Systems

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Statistical evaluation of snow accumulation and depletion from remotely sensed MODIS snow time series data using the SARIMA model

Kumar

Tiwari

Kumar

et al. 2023

Journal of Water Supply: Research and Technology-Aqua

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In the remote and challenging terrain of the Himalayan region, accurate measurement of cyclic snow accumulation and depletion is a significant challenge. To overcome this, an attempt has been made in the present study by applying a statistical analysis of MODIS snow time series data with the Seasonal Autoregressive Integrated Moving Average (SARIMA) model from 2003 to 2018 over the Beas river basin. The Box–Jenkins methodology of forecasting is based on the identification using seasonality, stationarity, ACF, and PACF plots; and estimation based on maximum likelihood techniques; and the last diagnostic checking based on the residual and error values have been used. Later, forecasting models have been proposed separately for the snow accumulation period (October–February) as (1,1,1) (0,1,3)19 and for the snow depletion period (March–September) as (1,1,1) (1,1,2)27 after calibration of the data (2003–2015) and the same were then validated using data (2016–2018). The accuracy assessment of the models has been checked using performance criteria like AIC, MSE, and RSS. The comparison of the forecasting models with the observed data showed a good agreement with R2 of 0.83 and 0.89 for snow accumulation and snow depletion, respectively. This research highlights the potential of utilizing satellite data and statistical modeling to address the challenges of monitoring snow cover in remote and inaccessible regions.

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Conjugate Gradient Methods for Computing Weighted Analytic Center for Linear Matrix Inequalities Using Exact and Quadratic Interpolation Line Searches

Cited by 3 publications

References 20 publications

A Weighted Analytic Center for Second-Order Cone Constraints

A Weighted Analytic Center for Second-Order Cone Constraints

Extracting Hidden Crime Patterns by Analysing Crime Dataset

Statistical evaluation of snow accumulation and depletion from remotely sensed MODIS snow time series data using the SARIMA model

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