Non Interior Point Supporting Hyperplane method for solving Mixed Integer Nonlinear Programming

Dalin; Chen Aruna

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Non Interior Point Supporting Hyperplane method for solving Mixed Integer Nonlinear Programming

Dalin 1 * #,Chen Aruna 2

1.School of Mathematical Science，Inner Mongolia University Huhehot, 010021

2.Mathematics Science College，Inner Mongolia Normal University，Huhehot 010022

*Correspondence author

#Submitted by

Subject:

Funding: Research Fund for doctoral program of Higher Education of China（No.2012501120004）

Opened online:22 May 2017

Accepted by: none

Citation: Dalin,Chen Aruna.Non Interior Point Supporting Hyperplane method for solving Mixed Integer Nonlinear Programming[OL]. [22 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4734001

In 1995 Westerlund and Pettersson proposed extended cutting plane (ECP) method for solving MINLP problems which is extended from Kelley's Cutting Plane (CP) method. The advantage of ECP method is simplicity and robustness of the solution and ECP method is suitable for solving large convex MINLP problems with moderate degree nonlinearity. In 1967 Veinott introduced a supporting hyperplane (SHP) method for solving NLP problems. Following the idea of ECP method, SHP method can be extended to solve MINLP problems. When SHP method is applied for solving MINLP problems, an interior point or a feasible solution must be gotten at first. However, finding a good feasible solution to a MINLP problem is difficult. So in this paper a new kind of SHP method, non interior point based SHP (NISHP) method，is introduced. A feasible solution is not required at the beginning in this method, and this method is more efficient than ECP method.

Keywords:operations research; Mixed Integer Nonlinear Programming; Cutting Plane Method; Supporting Hyperplane Method; steepest descent method

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