Estimates of the Duality Gap of Non-Convex Optimization Problems.

摘要

The difference between the optimal values of an optimization problem and its dual is called 'the duality gap'. Under convenient assumptions (the so-called constraint qualification assumptions), it is known that the length of the duality gap is equal to zero when the functions and the constraints are convex. The aim of this paper is prove estimates of the duality gap in terms of a convenient measure of the 'lack of convexity' of the functions involved in the optimization problem.