  Quasi-convex optimization acts a pivotal part in many fields including
economics and finance; the subgradient method is an effective iterative
algorithm for solving large-scale quasi-convex optimization problems. In this
paper, we investigate the iteration complexity and convergence rates of various
subgradient methods for solving quasi-convex optimization in a unified
framework. In particular, we consider a sequence satisfying a general (inexact)
basic inequality, and investigate the global convergence theorem and the
iteration complexity when using the constant, diminishing or dynamic stepsize
rules. More importantly, we establish the linear (or sublinear) convergence
rates of the sequence under an additional assumption of weak sharp minima of
H\"{o}lderian order and upper bounded noise. These convergence theorems are
applied to establish the iteration complexity and convergence rates of several
subgradient methods, including the standard/inexact/conditional subgradient
methods, for solving quasi-convex optimization problems under the assumptions
of the H\"{o}lder condition and/or the weak sharp minima of H\"{o}lderian
order.
