Mapping spectral colors in an Interim Connection Space (ICS) of a full spectral space based on an objective function is provided. A spectral color value in the ICS is accessed, and a spectral gamut boundary of the destination gamut is accessed. The spectral color value is mapped into mapped spectral color value based on minimization of an objective function of coordinates of a first subspace of the ICS, by fixing coordinates of a second subspace of the ICS, subject to a constraint that a result is within the spectral gamut boundary. The first subspace is a null space of a transformation from the ICS to a color space, while the second subspace is an orthogonal complement of the first subspace in the ICS. The constraint is determined by a gamut section that is an intersection of the spectral gamut in the ICS and an affine subspace characterized by the fixed coordinates of the second subspace.