A penalty approach for solving nonsmooth and nonconvex MINLP problems

This paper presents a penalty approach for globally solving nonsmooth and nonconvex mixed-integer nonlinear programming (MINLP) problems. Both integrality constraints and general nonlinear constraints are handled separately by hyperbolic tangent penalty functions. Proximity from an iterate to a feasible promising solution is enforced by an oracle penalty term. The numerical experiments show that the proposed oracle-based penalty approach is effective in reaching the solutions of the MINLP problems and is competitive when compared with other strategies.FCT - Fundação para a Ciência e a Tecnologia.The authors would like to thank two anonymous referees for their valuable comments and suggestions to improve the paper. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Fundação para a Ciência e a Tecnologia within the projects UID/CEC/00319/2013 and UID/MAT/00013/ 2013.