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Two-Segment Separable Programming

Author

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  • R. R. Meyer

    (University of Wisconsin-Madison)

Abstract

New iterative separable programming techniques based on two-segment, piecewise-linear approximations are described for the minimization of convex separable functions over convex sets. These techniques have two advantages over traditional separable programming methods. The first is that they do not require the cumbersome "fine grid" approximations employed to achieve high accuracy in the usual separable programming approach. In addition, the new methods yield feasible solutions with objective values guaranteed to be within any specified tolerance of optimality. In computational tests with real-world problems of up to 500 "nonlinear" variables the approach has exhibited rapid convergence and yielded very close bounds on the optimal value.

Suggested Citation

  • R. R. Meyer, 1979. "Two-Segment Separable Programming," Management Science, INFORMS, vol. 25(4), pages 385-395, April.
    • Handle: RePEc:inm:ormnsc:v:25:y:1979:i:4:p:385-395
    DOI: 10.1287/mnsc.25.4.385
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    Cited by:

    1. Lingxun Kong & Christos T. Maravelias, 2020. "On the Derivation of Continuous Piecewise Linear Approximating Functions," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 531-546, July.
    2. Aboolian, Robert & Berman, Oded & Krass, Dmitry, 2007. "Competitive facility location model with concave demand," European Journal of Operational Research, Elsevier, vol. 181(2), pages 598-619, September.
    3. Niederhoff, Julie A., 2007. "Using separable programming to solve the multi-product multiple ex-ante constraint newsvendor problem and extensions," European Journal of Operational Research, Elsevier, vol. 176(2), pages 941-955, January.
    4. Li, Han-Lin & Yu, Chian-Son, 1999. "A global optimization method for nonconvex separable programming problems," European Journal of Operational Research, Elsevier, vol. 117(2), pages 275-292, September.

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