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Concave envelopes of monomial functions over rectangles

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  • Harold P. Benson

Abstract

The construction of convex and concave envelopes of real‐valued functions has been of interest in mathematical programming for over 3 decades. Much of this interest stems from the fact that convex and concave envelopes can play important roles in algorithms for solving various discrete and continuous global optimization problems. In this article, we use a simplicial subdivision tool to present and validate the formula for the concave envelope of a monomial function over a rectangle. Potential algorithmic applications of this formula are briefly indicated. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

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  • Harold P. Benson, 2004. "Concave envelopes of monomial functions over rectangles," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 467-476, June.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:4:p:467-476
    DOI: 10.1002/nav.20011
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    References listed on IDEAS

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    1. Harold P. Benson, 1985. "A finite algorithm for concave minimization over a polyhedron," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 32(1), pages 165-177, February.
    2. James E. Falk & Richard M. Soland, 1969. "An Algorithm for Separable Nonconvex Programming Problems," Management Science, INFORMS, vol. 15(9), pages 550-569, May.
    3. H. P. Benson & G. M. Boger, 2000. "Analysis Of An Outcome Space Formulation Of The Multiplicative Programming Problem," World Scientific Book Chapters, in: Yong Shi & Milan Zeleny (ed.), New Frontiers Of Decision Making For The Information Technology Era, chapter 6, pages 100-122, World Scientific Publishing Co. Pte. Ltd..
    4. Richard M. Soland, 1974. "Optimal Facility Location with Concave Costs," Operations Research, INFORMS, vol. 22(2), pages 373-382, April.
    5. Faiz A. Al-Khayyal & James E. Falk, 1983. "Jointly Constrained Biconvex Programming," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 273-286, May.
    6. B. Kalantari & J. B. Rosen, 1987. "An Algorithm for Global Minimization of Linearly Constrained Concave Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 544-561, August.
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