In this paper, a new PSO algorithm with adaptive inertia weight is introduced for global optimization. The objective of the study is to balance local search and global search abilities and alternate them through the algorithm progress. For this, an adaptive inertia weight is introduced using a feedback on particles' best positions. The inertia weight keeps varying to alternate exploration and exploitation. Tests are carried on a set of thirty test functions (the CEC 2014 benchmark functions) and compared with other settings of inertia weight. Results show that the new algorithm is very competitive mainly when increasing the dimension of the search space.