The invention relates in particular to optimizing memory access in a microprocessor including several logic cores upon the resumption of executing a main application, and enabling the simultaneous execution of at least two processes in an environment including a hierarchically organized shared memory including a top portion and a bottom portion, a datum being copied from the bottom portion to the top portion for processing by the application. The computer is adapted to interrupt the execution of the main application. Upon an interruption in the execution of said application, a reference to a datum stored in a top portion of the memory is stored, wherein said datum must be used in order to enable the execution of the application. After programming a resumption of the execution of the application and before the resumption thereof, said datum is accessed in a bottom portion of the memory in accordance with the reference to be stored in a top portion of the memory.