This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and constraints possess certain patterns necessary for modeling real systems, a perfect dual problem (without duality gap) can be obtained in a unified form with global optimality conditions provided. While the popular augmented Lagrangian method may produce more difficult nonconvex problems due to the nonlinearity of constraints.
Canonical duality for solving general nonconvex constrained problems / Latorre, Vittorio; D. Y., Gao. - In: OPTIMIZATION LETTERS. - ISSN 1862-4472. - (In corso di stampa).
Canonical duality for solving general nonconvex constrained problems
LATORRE, VITTORIO;
In corso di stampa
Abstract
This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and constraints possess certain patterns necessary for modeling real systems, a perfect dual problem (without duality gap) can be obtained in a unified form with global optimality conditions provided. While the popular augmented Lagrangian method may produce more difficult nonconvex problems due to the nonlinearity of constraints.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.