Outer approximation with equality relaxation

Outer Approximation with Equality Relaxation, OA/ER (Kocis and Grossmann,... 

To handle explicitly nonlinear equality constraints of the form h(x) = 0, Kocis and Grossmann (1987) proposed the outer approximation with equality relaxation OA/ER algorithm for the following class of MINLP problems ... 

Section 6.5 presents the Outer Approximation with Equality Relaxation OA/ER for handling nonlinear equality constraints. Sections 6.5.1 and 6.5.2 discuss the formulation, assumptions and the basic idea. Section 6.5.3 discusses the equality relaxation, and illustrates it with a simple example, and presents the formulation of the master problem. Section 6.5.4 discusses the OA/ER algorithm and illustrates it with a small planning problem. 

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. 

Outer Approximation with Equality Relaxation and Augmented Penalty, OA/ER/AP, 168... 

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