This research paper deals with constraint logic programming, specifically with the CLP(R) language [1]. Starting with the remark that many applications of such a language require not only testing whether a set of constraints is satisfiable but also finding the optimal solution (or, more modestly, an approximation of the optimal solution), the authors show through elementary examples that declarative semantics and their immediate operational translations do not give correct answers.

The easiest way to the required global optimization is to optimize each subgoal during the derivation. The authors suggest three changes in the operational semantics: the current optimum is used to prune the search space, optimization subgoals are not selected until their global variables are grounded, and optimization subgoals return constraints when the optimal value occurs over a range of points.

By translating optimization to negation, one can give a declarative form to the modified operational semantics, which allows proofs of soundness and completeness results (in terms of three-valued logic). As is now usual in research papers, however, the proofs of the theorems are only outlined.

Last but not least: what kind of optimization is performed during the execution of such a program? The paper does not answer this question.