In this paper, we consider mixed-integer nonlinear constrained optimization problems. Specifically, we assume that the integrality constraints are non-relaxable, that is, the functions appearing in the problem cannot be computed when the integrality constraints are violated. To solve this class of problems, we propose an augmented Lagrangian-type algorithm which is able to handle integer variables by means of primitive directions. A theoretical analysis of the convergence properties of the proposed algorithm is carried out. Finally, some numerical experimentation is reported.
An Augmented Lagrangian-Based Method Using Primitive Directions for Mixed-Integer Nonlinear Problems / Cristofari, Andrea; Di Pillo, Gianni; Liuzzi, Giampaolo; Lucidi, Stefano. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 209:2(2026). [10.1007/s10957-026-02981-9]
An Augmented Lagrangian-Based Method Using Primitive Directions for Mixed-Integer Nonlinear Problems
Di Pillo, GianniMembro del Collaboration Group
;Liuzzi, Giampaolo
Membro del Collaboration Group
;Lucidi, StefanoMembro del Collaboration Group
2026
Abstract
In this paper, we consider mixed-integer nonlinear constrained optimization problems. Specifically, we assume that the integrality constraints are non-relaxable, that is, the functions appearing in the problem cannot be computed when the integrality constraints are violated. To solve this class of problems, we propose an augmented Lagrangian-type algorithm which is able to handle integer variables by means of primitive directions. A theoretical analysis of the convergence properties of the proposed algorithm is carried out. Finally, some numerical experimentation is reported.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
