515 research outputs found
A smoothing Newton method for minimizing a sum of Euclidean norms
2000-2001 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe
Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent
First-order methods play a central role in large-scale machine learning. Even
though many variations exist, each suited to a particular problem, almost all
such methods fundamentally rely on two types of algorithmic steps: gradient
descent, which yields primal progress, and mirror descent, which yields dual
progress.
We observe that the performances of gradient and mirror descent are
complementary, so that faster algorithms can be designed by LINEARLY COUPLING
the two. We show how to reconstruct Nesterov's accelerated gradient methods
using linear coupling, which gives a cleaner interpretation than Nesterov's
original proofs. We also discuss the power of linear coupling by extending it
to many other settings that Nesterov's methods cannot apply to.Comment: A new section added; polished writin
Stochastic Multifacility Location Problem under Triangular Area Constraint with Euclidean Norm
The multifacility location issue is an augmentation of the single-location problem in which we might be keen on finding the location of various new facilities concerning different existing locations. In the present study, multifacility location under triangular zone limitation with probabilistic methodology for the weights considered in the objective function and the Euclidean distances between the locations has been presented. Scientific detailing and the explanatory arrangement have been acquired by utilizing Kuhn-Tucker conditions. The arrangement strategy has been represented with the assistance of a numerical illustration. Two sub-instances of the issue in each of which the new locations are to be situated in semi-open rectangular zone have likewise been talked about
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