Augmented penalty/equality relaxation

Viswanathan and Grossmann (1990) proposed introducing slacks in the MILP master problem to reduce the likelihood of cutting off feasible solutions. This master problem (augmented penalty/equality relaxation) (APER) has the following form ... 

The MINLP-problems were implemented in GAMS [7, 8] and solved by the outer approximation/equality relaxation/augmented penalty-method [9] as implemented in DICOPT. The algorithm generates a series of NLP and MILP subproblems, which were solved by the generalized reduced gradient method [10] as implemented in CONOPT and the integrality relaxation based branch and cut method as... 

Outer Approximation/Equality Relaxation/Augmented Penalty... 

Outer Approximation with Equality Relaxation and Augmented Penalty, OA7ER/AP (Viswanathan and Grossmann, 1990)... 

Section 6.6 discusses the Outer Approximation with Equality Relaxation and Augmented Penalty OA/ER/AP approach. In Sections 6.6.1 and 6.6.2 the formulation and basic idea are presented, while in section 6.6.3 the master problem is derived. Section 6.6.4 presents the OA/ER/AP algorithm and illustrates it with a nonconvex example problem. The reader is referred to the suggested references in sections 6.4,6.5 and 6.6 for further reading in the outer approximation based algorithms. 

MINOPT (Mixed Integer Nonlinear OPTimizer) is written entirely in C and solves MINLP problems by a variety of algorithms that include (i) the Generalized Benders Decomposition GBD, (ii) the Outer Approximation with Equality Relaxation OA/ER, (iii) the Outer Approximation with Equality Relaxation and Augmented Penalty OA/ER/AP, and (iv) the Generalized Cross Decomposition GCD. 

Once an initial solution is incorporated into the MINLP model, the model is solved via the DICOPT solver employing the Outer approximation algorithm for equality relaxation and augmented penalty (OA/ER/AP). 

---