6,937 research outputs found
Accelerated Methods for -Weakly-Quasi-Convex Problems
Many problems encountered in training neural networks are non-convex.
However, some of them satisfy conditions weaker than convexity, but which are
still sufficient to guarantee the convergence of some first-order methods. In
our work we show that some previously known first-order methods retain their
convergence rates under these weaker conditions
A new, globally convergent Riemannian conjugate gradient method
This article deals with the conjugate gradient method on a Riemannian
manifold with interest in global convergence analysis. The existing conjugate
gradient algorithms on a manifold endowed with a vector transport need the
assumption that the vector transport does not increase the norm of tangent
vectors, in order to confirm that generated sequences have a global convergence
property. In this article, the notion of a scaled vector transport is
introduced to improve the algorithm so that the generated sequences may have a
global convergence property under a relaxed assumption. In the proposed
algorithm, the transported vector is rescaled in case its norm has increased
during the transport. The global convergence is theoretically proved and
numerically observed with examples. In fact, numerical experiments show that
there exist minimization problems for which the existing algorithm generates
divergent sequences, but the proposed algorithm generates convergent sequences.Comment: 22 pages, 8 figure
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