The Monotonicity Principles are only necessary conditions. All principles are under the condition “if the problem is well constrained”. But one of the important purposes of Monotonicity Analysis is to identify optimization models that are not well constrained. Before applying Monotonicity Principles to a problem, whether the problem is well constrained is not known. This paper attempts to clarify some potential problems of Monotonicity Analysis when applying to not-well-constrained problems. These problems can be easily explained using the Karush-Kuhn-Tucker optimality conditions. Ways to prevent the users from reaching erroneous results in these situations are proposed. These results are implemented in the computer program MONO. MONO is a logic program which automatically generates rigorous Monotonicity Analysis steps and global facts about the optimization model. Hardware and software requirements of this program are minimal. A hydraulic cylinder design example is used to demonstrate the program.

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