Crandi

Pdf New Adaptive Barzilai Borwein Step Size And Its Application In Sol

Leo Migdal
-
pdf new adaptive barzilai borwein step size and its application in sol

Published online by Cambridge University Press: 03 December 2018 We propose a new adaptive and composite Barzilai–Borwein (BB) step size by integrating the advantages of such existing step sizes. Particularly, the proposed step size is an optimal weighted mean of two classical BB step sizes and the weights are updated at each iteration in accordance with the quality of the classical BB step... Combined with the steepest descent direction, the adaptive and composite BB step size is incorporated into the development of an algorithm such that it is efficient to solve large-scale optimization problems. We prove that the developed algorithm is globally convergent and it R-linearly converges when applied to solve strictly convex quadratic minimization problems. Compared with the state-of-the-art algorithms available in the literature, the proposed step size is more efficient in solving ill-posed or large-scale benchmark test problems.

View all Google Scholar citations for this article. To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your... Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about saving to your Kindle. Note you can select to save to either the @free.kindle.com or @kindle.com variations.

‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community?

Learn more about arXivLabs. Journal of Industrial and Management Optimization School of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China This work is funded by the National Natural Science Foundation of China (grant number 12371099). The Barzilai-Borwein(BB) method is an effective gradient descent algorithm for solving unconstrained optimization problems. Based on the observation of two classical BB step sizes and by constructing an interpolated least squares model, we propose a novel class of BB step sizes.

Each member of this class retains the quasi-Newton property, with the original two BB step sizes being its extreme cases. We present the mathematical principle underlying the adaptive alternating BB (ABB) method. Based on this principle, we develop a class of effective adaptive interpolation parameters. For strictly convex quadratic optimization problems, we establish the $ R $-linear convergence of this new gradient descent method by investigating the evolution pattern of the ratio of the absolute values of the gradient... Numerical experiments are conducted to illustrate our findings. Figure 1.

The horizontal axis is $ \alpha_{k} $, and the vertical axis is the value of $ \phi(\alpha_{k}) $

People Also Search

Published Online By Cambridge University Press: 03 December 2018 We

Published online by Cambridge University Press: 03 December 2018 We propose a new adaptive and composite Barzilai–Borwein (BB) step size by integrating the advantages of such existing step sizes. Particularly, the proposed step size is an optimal weighted mean of two classical BB step sizes and the weights are updated at each iteration in accordance with the quality of the classical BB step... Com...

View All Google Scholar Citations For This Article. To Send

View all Google Scholar citations for this article. To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your... Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about...

‘@free.kindle.com’ Emails Are Free But Can Only Be Saved To

‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have em...

Learn More About ArXivLabs. Journal Of Industrial And Management Optimization

Learn more about arXivLabs. Journal of Industrial and Management Optimization School of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China This work is funded by the National Natural Science Foundation of China (grant number 12371099). The Barzilai-Borwein(BB) method is an effective gradient descent algorithm for solving unconstrained optimization problems. Based ...

Each Member Of This Class Retains The Quasi-Newton Property, With

Each member of this class retains the quasi-Newton property, with the original two BB step sizes being its extreme cases. We present the mathematical principle underlying the adaptive alternating BB (ABB) method. Based on this principle, we develop a class of effective adaptive interpolation parameters. For strictly convex quadratic optimization problems, we establish the $ R $-linear convergence ...