This article investigates the two paradigms of norm optimal iterative learning control (NOILC) and parameter optimal iterative learning control (POILC) for multivariable (MIMO) l-input, m-output linear discrete-time systems. The main result is a proof that, despite their algebraic and conceptual differences, they can be unified using linear quadratic multi-parameter optimisation techniques. In particular, whilst POILC has been naturally regarded as an approximation to NOILC, it is shown that the NOILC control law can be generated from a suitable choice of control law parameterisation and objective function in a multi-parameter MIMO POILC problem. The form of this equivalence is used to propose a new general approach to the construction of POILC problems for MIMO systems that approximates the solution of a given NOILC problem. An infinite number of such approximations exist. This great diversity is illustrated by the derivation of new convergent algorithms based on time interval and gradient partition that extend previously published work.