Constraint Activity Revisited: Application to Global and Discrete Design Optimization

The concept of constraint activity, widely used throughout the optimization literature, is extended and clarified to deal with global optimization problems containing either continuous or discrete variables. The article begins by presenting definitions applicable to individual constraints, followed by definitions of groups of constraints. Concepts are reinforced through the use of examples. The definitions are used to investigate the ideas of degrees of freedom, optimization “cases,” and monotonicity analysis, as applied to global and discrete problems. Applicability to local optimization is also noted.