  The co-localization problem is a model that simultaneously localizes objects
of the same class within a series of images or videos. In
\cite{joulin2014efficient}, authors present new variants of the Frank-Wolfe
algorithm (aka conditional gradient) that increase the efficiency in solving
the image and video co-localization problems. The authors show the efficiency
of their methods with the rate of decrease in a value called the Wolfe gap in
each iteration of the algorithm. In this project, inspired by the conditional
gradient sliding algorithm (CGS) \cite{CGS:Lan}, We propose algorithms for
solving such problems and demonstrate the efficiency of the proposed algorithms
through numerical experiments. The efficiency of these methods with respect to
the Wolfe gap is compared with implementing them on the YouTube-Objects dataset
for videos.
