A New Successive Partition Algorithm for Concave Minimization Based on Cone Decomposition and Decomposition Cuts

Authors:
Marcus Porembski
Affiliations:
University of Marburg, Department of Mathematics, 35032 Marburg, Germany (e-mail: porembski@t-online.de)
Venue:
Journal of Global Optimization
Year:
2004

Citing 5
Cited 1

A composite branch and bound, cutting plane algorithm for concave minimization over a polyhedron

Computers and Operations Research
Generalized &agr;-valid cut procedure for concave minimization

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A Simplified Convergence Proof for the Cone Partitioning Algorithm

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How to Extend the Concept of Convexity Cuts to Derive Deeper Cutting Planes

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Finite Exact Branch-and-Bound Algorithms for Concave Minimization over Polytopes

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A Cutting-Surface Method for Uncertain Linear Programs with Polyhedral Stochastic Dominance Constraints

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Abstract

In this paper we propose a new partition algorithm for concave minimization. The basic structure of the algorithm resembles that of conical algorithms. However, we make extensive use of the cone decomposition concept and derive decomposition cuts instead of concavity cuts to perform the bounding operation. Decomposition cuts were introduced in the context of pure cutting plane algorithms for concave minimization and has been shown to be superior to concavity cuts in numerical experiments. Thus by using decomposition cuts instead of concavity cuts to perform the bounding operation, unpromising parts of the feasible region can be excluded from further explorations at an earlier stage. The proposed successive partition algorithm finds an ϵ-global optimal solution in a finite number of iterations.