Remarks on Sufficiency of Constraint-Bound Solutions in Optimal Design

Abstract

Early preliminary models for optimal design problems in nonlinear programming formulations often have solutions that are constraint-bound points, i.e., the number of active constraints equals the number of design variables. Models leading to such solutions will typically offer little insight to design trade-offs, and it is desirable to identify them early in order to revise the model or to exclude the points from an active set strategy. Application of monotonicity analysis can quickly identify constraint-bound candidate solutions but not always prove their optimality. This article discusses some conditions under which these points are in fact global or local optima.