We establish local well-posedness in the sense of Hadamard for the higher-order nonlinear Schrödinger equation with a general power nonlinearity formulated on the half-line. We consider two different scenarios of certain parameters, one of which is associated with a single boundary condition, and the other case requires the use of two boundary conditions. We assume general nonhomogeneous Dirichlet and/or Neumann boundary conditions. Our functional framework centers around fractional Sobolev spaces with respect to the spatial variable. We treat both high regularity and low regularity solutions: in the former setting, the relevant nonlinearity can be handled via the Banach algebra property; in the latter setting, however, this is no longer the case and, instead, delicate Strichartz estimates must be established. This task is especially challenging in the framework of nonhomogeneous initial-boundary value problems, as it involves proving boundary-type Strichartz estimates that are not common in the study of Cauchy (initial value) problems. The linear analysis, which forms the core of this work, crucially relies on a weak solution formulation defined through the novel solution formulae obtained via the Fokas method (also known as the unified transform) for the associated forced linear problem. In this connection, we note that the higher-order Schrödinger equation comes with an increased level of difficulty due to the presence of more than one spatial derivatives in the linear part of the equation. This feature manifests itself via several complications throughout the analysis, including (i) analyticity issues related to complex square roots, which require careful treatment of branch cuts and deformations of integration contours; (ii) singularities that emerge upon changes of variables in the Fourier analysis arguments; (iii) complicated oscillatory kernels in the weak solution formula for the linear initial-boundary value problem, which require a subtle analysis of the dispersion in terms of the regularity of the boundary data. *This is a joint work with A. Alkın (Iztech) and D. Mantzavinos (Univ. of Kansas).