Distance-to-Solution Estimates for Optimization Problems with Constraints in Standard Form

An important tool in the formulation and analysis of algorithms for constrained optimization is a quantity that provides a practical estimate of the distance to the set of primal-dual solutions. Such ``distance-to-solution estimates'' may be used to identify the inequality constraints satisfied with equality at a solution, and to formulate conditions used to terminate a sequence of solution estimates. This note concerns the properties of a particular distance-to-solution estimate for optimization problems with constraints written in so-called ``standard form'', which is a commonly-used approach for formulating constraints with a mixture of equality and inequality constraints.

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