A study of the kinematics of the Galaxy includes calculating quantities such as the Oort A and B constants, the K term, the solar velocity, and others as well as the velocity ellipsoid. Usually the ellipsoid is calculated separately. A disadvantage of separate calculations for the kinematical parameters and the velocity ellipsoid arises from both calculations including the solar velocity. This quantity will not be the same from the kinematical calculations as from the calculations for the velocity ellipsoid. But if we perform a simultaneous adjustment for the kinematical parameters and the velocity ellipsoid using the recently developed (during the decade of the 90's) mathematical technique of semi-definite programming (SDP), we can impose the condition that both the kinematical and the velocity ellipsoid calculations give the same solar velocity. SDP also possesses the property that the ellipsoid calculated is unique and represents a global minimum of the adjustment criterion when that criterion is either the robust L1 criterion or the difference of squares (DOS) criterion. DOS is related to, but not identical with, least squares. A simultaneous adjustment using SDP is applied to 290 O-B5 III stars, of which 107 have radial velocities, and 1563 M III stars, of which 453 have radial velocities, with the data taken from the Hipparcos, Wilson, and Barbier-Brossat catalogs. Reasonable results are obtained. The O-B5 stars show a lower solar motion and nearer equality of the A and B constants than the M III stars. The dispersions of the velocity ellipsoid are higher for the M III stars. The velocity ellipsoid for the O-B5 stars shows a significant tilt with respect to the Galactic plane. Although the dispersions of the velocity ellipsoid are higher than those generally given, this is a consequence of use of the DOS criterion rather than the more often used method of moments. Given that DOS calculates a unique ellipsoid, one can argue that the dispersions are in reality superior to those given by the method of moments.