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A Finite Algorithm for Global Minimization of Separable Concave Programs

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Abstract

Researchers first examined the problem of separable concave programming more than thirty years ago, making it one of the earliest branches of nonlinear programming to be explored. This paper proposes a new algorithm that finds the exact global minimum of this problem in a finite number of iterations. In addition to proving that our algorithm terminates finitely, the paper extends a guarantee of finiteness to all branch-and-bound algorithms for concave programming that (1) partition exhaustively using rectangular subdivisions and (2) branch on the incumbent solution when possible. The algorithm uses domain reduction techniques to accelerate convergence; it solves problems with as many as 100 nonlinear variables, 400 linear variables and 50 constraints in about five minutes on an IBM RS/6000 Power PC. An industrial application with 152 nonlinear variables, 593 linear variables, and 417 constraints is also solved in about ten minutes.

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Authors and Affiliations

  1. Department of Mechanical & Industrial Engineering and, The University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, IL, 61801, U.S.A

    J. Parker Shectman

  2. Department of Chemical Engineering, The University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, IL, 61801, U.S.A

    Nikolaos V. Sahinidis

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  1. J. Parker Shectman
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Correspondence to Nikolaos V. Sahinidis.

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Shectman, J.P., Sahinidis, N.V. A Finite Algorithm for Global Minimization of Separable Concave Programs. Journal of Global Optimization 12, 1–36 (1998). https://doi.org/10.1023/A:1008241411395

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