Next, the algorithm solves the subproblem by considering the entire set of customers.
Guillermo Cabrera G., Enrique Cabrera, Ricardo Soto, L. Jose Miguel Rubio, BroderickCrawford, Fernando Paredes 2012, 'A Hybrid Approach Using an Artificial Bee Algorithm with Mixed Integer ProgrammingApplied to a Large-Scale Capacitated Facility Location Problem', Mathematical Problems in Engineeringhttp://dx.doi.org/10.1155/2012/954249. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
At each iteration, it needs low storage and the subproblem can be easily solved.
Dexiang Feng, Min Sun, Xueyong Wang 2017, 'A family of conjugate gradient methods for large-scale nonlinear equations', Journal of Inequalities and Applicationshttp://link.springer.com/article/10.1186/s13660-017-1510-0. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
At every iteration, we need to calculate a second-order cone subproblem.
Ying Ji, Tienan Wang, Yijun Li 2014, 'A Continuous Trust-Region-Type Method for Solving Nonlinear Semidefinite ComplementarityProblem', Abstract and Applied Analysishttp://dx.doi.org/10.1155/2014/589731. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In each iteration, we solve this unconstrained subproblem to obtain the trial step.
Hao Zhang, Qin Ni 2017, 'A New Augmented Lagrangian Method for Equality Constrained Optimization with SimpleUnconstrained Subproblem', Discrete Dynamics in Nature and Societyhttp://dx.doi.org/10.1155/2017/6406514. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Even the subproblem of defining the criteria under which to classify news as “fake” creates ambiguity that requires human judgment.
Jow Meiling, Shiao Yaojung 2018, 'Smart Learning of Porn Fake News in the Family-Friendly Filters', MATEC Web of Conferenceshttps://doi.org/10.1051/matecconf/201820104004. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In this paper we focus on one particular parameter, which determines the size of the subproblem.
Guillermo Cabrera-Guerrero, Carolina Lagos, Carolina Castañeda, Franklin Johnson,Fernando Paredes, Enrique Cabrera 2017, 'Parameter Tuning for Local-Search-Based Matheuristic Methods', Complexityhttp://dx.doi.org/10.1155/2017/1702506. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
A master problem determines the assignment of platforms to wells and a planning subproblem calculates the timing for fixed assignments.
M.C.A. Carvalho, J.M. Pinto 2006, 'A bilevel decomposition technique for the optimal planning of offshore platforms',Brazilian Journal of Chemical Engineeringhttp://www.scielo.br/scielo.php?script=sci_arttext&pid=S0104-66322006000100008. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We generalize the fast alternating direction method to solve the proposed model so that every subproblem can be easily solved.
Weifeng Zhou, Hua Xiang 2017, 'Frame-Based CT Image Reconstruction via the Balanced Approach', Journal of Healthcare Engineeringhttp://dx.doi.org/10.1155/2017/1417270. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Exhaustive searches show that, for small-sized tori, each of the proposed schemes produces an optimal solution to the corresponding subproblem.
Xiaofan Yang, Pengdeng Li, Lu-Xing Yang, Yingbo Wu 2016, 'Reducing the Spectral Radius of a Torus Network by Link Removal', PLOS ONE10.1371/journal.pone.0155580. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We reduce the constrained problem to unconstrained linear least squares and partition it into a small subproblem.
Salman Zeb, Muhammad Yousaf 2017, 'Updating QR factorization procedure for solution of linear least squares problem withequality constraints', Journal of Inequalities and Applicationshttp://link.springer.com/article/10.1186/s13660-017-1547-0. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)