PRIMA: A Production-Based Implicit Elimination System for Monotonicity Analysis of Optimal Design Models

Monotonicity analysis is a useful method for analyzing optimal design models prior to numerical computation. Much of the information required for such analysis is represented in the monotonicity table. Rigorous procedures using the monotonicity principles and the implicit function theorem have been combined with heuristics, to extract additional constraint activity knowledge based only on the information contained in the monotonicity table. PRIMA is a production system implemented in the OPS5 programming environment. The system receives as input the monotonicity table of the initial model and derives global facts about boundedness and constraint activity by heuristic search of sequences of successively reduced models. Such reduction is obtained by implicit elimination of active constraints. Global facts generated automatically by this reasoning system can be used either for a global solution, or for a combined local-global active set strategy.