Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Lower and Upper Bounds in Smooth Strongly Convex Optimization - A
  Unified Approach via Linear Iterative Methods   In this thesis we develop a novel framework to study smooth and strongly
convex optimization algorithms, both deterministic and stochastic. Focusing on
quadratic functions we are able to examine optimization algorithms as a
recursive application of linear operators. This, in turn, reveals a powerful
connection between a class of optimization algorithms and the analytic theory
of polynomials whereby new lower and upper bounds are derived. In particular,
we present a new and natural derivation of Nesterov's well-known Accelerated
Gradient Descent method by employing simple 'economic' polynomials. This rather
natural interpretation of AGD contrasts with earlier ones which lacked a
simple, yet solid, motivation. Lastly, whereas existing lower bounds are only
valid when the dimensionality scales with the number of iterations, our lower
bound holds in the natural regime where the dimensionality is fixed.

35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio