  The task assignment problem is fundamental in combinatorial optimisation,
aiming at allocating one or more tasks to a number of agents while minimizing
the total cost or maximizing the overall assignment benefit. This problem is
known to be computationally hard since it is usually formulated as a
mixed-integer programming problem. In this paper, we consider a novel
time-triggered dimension reduction algorithm (TTDRA). We propose
convexification approaches to convexify both the constraints and the cost
function for the general non-convex assignment problem. The computational speed
is accelerated via our time-triggered dimension reduction scheme, where the
triggering condition is designed based on the optimality tolerance and the
convexity of the cost function. Optimality and computational efficiency are
verified via numerical simulations on benchmark examples.
