Solving convex mixed integer nonlinear programming optimization problems using a sequential cutting plane algorithm

Solving convex mixed integer nonlinear programming optimization problems using a sequential cutting plane algorithm

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Article ID: iaor2007396
Country: Netherlands
Volume: 34
Issue: 1
Start Page Number: 63
End Page Number: 83
Publication Date: May 2006
Journal: Computational Optimization and Applications
Authors: ,
Keywords: programming: branch and bound, programming: integer
Abstract:

In this article we look at a new algorithm for solving convex mixed integer nonlinear programming problems. The algorithm uses an integrated approach, where a branch and bound strategy is mixed with solving nonlinear programming problems at each node of the tree. The nonlinear programming problems, at each node, are not solved to optimality, rather one iteration step is taken at each node and then branching is applied. A Sequential Cutting Plane (SCP) algorithm is used for solving the nonlinear programming problems by solving a sequence of linear programming problems. The proposed algorithm generates explicit lower bounds for the nodes in the branch and bound tree, which is a significant improvement over previous algorithms based on QP techniques. Initial numerical results indicate that the described algorithm is a competitive alternative to other existing algorithms for these types of problems.

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