Math. Program., Ser. B (2018) 168:369–400
FULL LENGTH PAPER
Strong duality and KKT conditions in nonconvex
optimization with a single equality constraint
and geometric constraint
· Fabián Flores-Bazán
Received: 4 December 2015 / Accepted: 5 October 2016 / Published online: 15 October 2016
© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2016
Abstract Some topological and geometric characterizations of strong duality for a
non convex optimization problem under a single equality and geometric constraints
are established. In particular, a hidden convexity of the conic hull of joint-range of the
pair of functions associated to the original problem, is obtained. Applications to derive
(a characterization of the validity of) KKT conditions without standard constraints
qualiﬁcation, are also discussed. It goes beyond the exact penalization technique.
Several examples showing our results provide much more information than those
appearing elsewhere, are given. Finally, the standard quadratic problem involving a
non necessarily polyhedral cone is analyzed in detail.
Keywords Strong duality · Nonconvex optimization · Hidden convexity · Quadratic
programming · KKT conditions
Mathematics Subject Classiﬁcation Primary 90C20 · 90C46 · 49N10 · 49N15 ·
The research for the second author was supported in part by CONICYT-Chile through FONDECYT
115-0973 and BASAL Projects, CMM, Universidad de Chile.
Departamento de Ingeniería Matemática, CI2MA, Universidad de Concepción, Casilla 160-C,
Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción,