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

by Philip E. Gill, Vyacheslav Kungurtsev, Daniel P. Robinson


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.

UCSD-CCoM-16-01.pdf   April 2016