Goal programming has now become an important tool in areas such as public management science. There is therefore a need for examining ways of securing improved computational efficiency, as is done in this paper, instead of resting only on the linear programming equivalences that were set forth when the original goal programming article was published in Vol. 1, No. 2 of Management Science. Based on lemmata which permit reduction of various important classes of convex goal programming models to problems of full row rank-interval programming type, explicit solutions to convex goal programming problems are exhibited. Some of the equivalences herein established are also useful in their own right and for other classes of problems--e.g., interval programming--as well as advanced start procedures and other such computational matters.