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Vietnam Journal of Mathematics 35:4(2007) 333-414

 Comparison of Search Strategies of Branch and Bound Algorithm for Concave Minimization Problems Under Linear Constraints

Hiroshi Konno, Kazuo Izumi, and Rei Yamamoto

Abstract.  Solving large scale concave minimization problems is attracting more attention in recent years. A number of large scale practical problems have been solved to optimality by a branch and bound algorithm based on hyper-rectangular subdivision/linear under-estimating function and by a 0-1 mixed linear integer programming algorithm.We will report the result of a systematic comparison of search strategies of branch and bound algorithm. Also,we compare them with 0-1 integer programming approach.We will show that a depth first search strategy is useful for solving a very large scale mean-absolute deviation portfolio optimization problem under concave transaction cost.

Keywords: Global optimization, concave minimization, branch and bound algorithm, mixed 0-1 programming, portfolio optimization, mean-absolute deviation model.

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Published by Springer since January 2013