Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Iteration-complexity and asymptotic analysis of steepest descent method
  for multiobjective optimization on Riemannian manifolds   The steepest descent method for multiobjective optimization on Riemannian
manifolds with lower bounded sectional curvature is analyzed in this paper. The
aim of the paper is twofold. Firstly, an asymptotic analysis of the method is
presented with three different finite procedures for determining the stepsize,
namely, Lipschitz stepsize, adaptive stepsize and Armijo-type stepsize. The
second aim is to present, by assuming that the Jacobian of the objective
function is componentwise Lipschitz continuous, iteration-complexity bounds for
the method with these three stepsizes strategies. In addition, some examples
are presented to emphasize the importance of working in this new context.
Numerical experiments are provided to illustrate the effectiveness of the
method in this new setting and certify the obtained theoretical results.

20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th