  Inspired by the work of [Fang et al.. An improved annealing method and its
large-time behaviour. Stochastic Process. Appl. (1997), Volume 71 Issue 1 Page
55-74.], who propose an improved simulated annealing algorithm based on a
variant of overdamped Langevin diffusion with state-dependent diffusion
coefficient, we cast this idea in the kinetic setting and develop an improved
kinetic simulated annealing (IKSA) method for minimizing a target function $U$.
To analyze its convergence, we utilize the framework recently introduced by
[Monmarch\'{e}. Hypocoercivity in metastable settings and kinetic simulated
annealing. Probab. Theory Related Fields (2018), Volume 172 Page 1215-1248.]
for the case of kinetic simulated annealing (KSA). The core idea of IKSA rests
on introducing a parameter $c > \inf U$, which de facto modifies the
optimization landscape and clips the critical height in IKSA at a maximum of $c
- \inf U$. Consequently IKSA enjoys improved convergence with faster
logarithmic cooling than KSA. To tune the parameter $c$, we propose an adaptive
method that we call IAKSA which utilizes the running minimum generated by the
algorithm on the fly, thus avoiding the need to manually adjust $c$ for better
performance. We present positive numerical results on some standard global
optimization benchmark functions that verify the improved convergence of IAKSA
over other Langevin-based annealing methods.
