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Variations and extension of the convex–concave procedure

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Abstract

We investigate the convex–concave procedure, a local heuristic that utilizes the tools of convex optimization to find local optima of difference of convex (DC) programming problems. The class of DC problems includes many difficult problems such as the traveling salesman problem. We extend the standard procedure in two major ways and describe several variations. First, we allow for the algorithm to be initialized without a feasible point. Second, we generalize the algorithm to include vector inequalities. We then present several examples to demonstrate these algorithms.

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Acknowledgments

We would like to thank our many reviewers for their comments which improved this paper and in particular for highlighting much of the recent work in DCA. This research was made possible by the National Science Foundation Graduate Research Fellowship, Grant DGE-1147470 and by the Cleve B. Moler Stanford Graduate Fellowship.

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  1. Stanford University, Packard Building, Room 243, 350 Serra Mall, Stanford, CA, 94305, USA

    Thomas Lipp

  2. Stanford University, Packard Building, Room 254, 350 Serra Mall, Stanford, CA, 94305, USA

    Stephen Boyd

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Lipp, T., Boyd, S. Variations and extension of the convex–concave procedure. Optim Eng 17, 263–287 (2016). https://doi.org/10.1007/s11081-015-9294-x

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