Activity analysis: Simplifying optimal design problems through qualitative partitioning

Activity analysis is introduced as a means to strategically cut away subspaces of a design problem that can quickly be ruled out as suboptimal. This results in focused regions of the space in which additional symbolic or numerical analysis can take place. Activity analysis is derived from a qualitative abstraction of the Karush–Kuhn–Tucker conditions of optimality, used to partition an optimization problem into regions which are nonstationary and qualitatively stationary. Activity analysis draws from the fields of gradient-based optimization, conflict-based approaches of combinatorial satisfying search, and monotonicity analysis.