  Continuous Matrix Product States (cMPS) are powerful variational ansatz
states for ground states of continuous quantum field theories in (1+1)
dimension. In this paper we introduce a novel parametrization of the cMPS wave
function based on basis-spline functions, which we coin spline-based MPS
(spMPS), and develop novel regauging techniques for inhomogeneous cMPS. We
extend a recently developed ground-state optimization algorithm for
translational invariant cMPS [M. Ganahl, J. Rinc\'on, G.Vidal. Phys.Rev.Lett.
118,220402 (2017)] to the case of inhomogeneous cMPS and, as
proof-of-principle, use it to obtain the ground-state of a gas of Lieb-Liniger
bosons in a periodic potential. The proposed method provides a first working
implementation of a cMPS optimization for non-translational invariant
continuous Hamiltonians.
