Cutting plane methods

Westerlund, T. H. Skrifvars I. Harjunkoski, and R. Pom. An Extended Cutting Plane Method for a Class of Non-convex MINLP Problems. Comput Chem Eng 22 357-365 (1998). 

In the cutting plane methods, the feasible region is not divided into subdomains but instead new constraints, denoted as cuts, are generated and added which reduce the feasible region until a 0-1 optimal solution is obtained. 

Kelley, J. E.. Jr.. The Cutting-Plane Method for Solving Convex Programs, J. SIAM 8, 703-712 (I960). 

Westerlund, T., and Pettersson, F. A Cutting Plane Method for Solving Convex MINLP Problems. Report 92-124-A. Process Design Laboratory, Abo Akademi, 1992. 

Kelley J.E. Jr. 1960. The cutting-plane method for solving convex programs, J. SIAM, 8, 703. 

Sawaya N.W. and Grossmann I.E. 2004. A cutting plane method for solving linear-generalized disjunctive programming problems (submitted). 

Cutting plane method. In this method, tool path curves are defined by intersecting a group of parallel planes (cutting planes)... 

Westerliind, T. and Lundqvist, K. (2003) Alpha-ECP, Version 5.04. An interactive MINLP-solver based on the extended cutting plane method Report 01-178-A, Process Design Laboratory, Abo Akademi University Abo, Finlande. 

Westerliind, T. and Petterson, F. (1995) A cutting plane method for solving convex MINLP problems. Computers Chemical Engineering, 19, S131-136. 

To solve the problem above the branch and bound method (see e.g. [106]), generalized Benders Decomposition [108], Outer Approximation [109, 110], LP/NLP branch and bound [111] and Extended Cutting Plane Method [112] are in use. Grossmann and Kravanja [113] give an extensive compilation of literature on MINLP problems. 

R. G. Jeroslow. Cutting plane theory Disjunctive methods. Ann. of Discrete Math., 1 293, 1977. 

This procedure for generating the cutting plane can be used by solving the separation problem (SP) only at the root node. It can also be used to strengthen the MINLP problem (BM) before applying methods such as OA, GBD, and ECP. It is also interesting to... 

Albunia, A. R., Milano, G, Venditto, V., Guerra, G. Clear-cut experimental method to discriminate between in-plane and out-of-plane molecular transition moments./. Am. Chem. 5 oc., 127,13114-13115 (2005). 

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