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Solution of and bounding in a linearly constrained optimization problem with convex, polyhedral objective function

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Abstract

A dual method is presented to solve a linearly constrained optimization problem with convex, polyhedral objective function, along with a fast bounding technique, for the optimum value. The method can be used to solve problems, obtained from LPs, where some of the constraints are not required to be exactly satisfied but are penalized by piecewise linear functions, which are added to the objective function of the original problem. The method generalizes an earlier solution technique developed by Prékopa (1990). Applications to stochastic programming are also presented.

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References

  1. R.G. Bland, “New finite pivoting rule for the simplex method,”Mathematics of Operations Research 2 (1977) 103–107.

    Google Scholar 

  2. G.B. Dantzig and A. Madansky, “On the solution of two-stage linear programs under uncertainty,”Proceedings of the Fourth Berkeley Symposium on Statistics and Probability 1 (University of California Press, Berkeley, CA, 1961) pp. 165–176.

    Google Scholar 

  3. C. Lemke, “The dual method for solving the linear programming problem,”Naval Research Logistic Quarterly 1 (1954) 36–47.

    Google Scholar 

  4. I. Lustig, R. Marsten and D. Shanno, “Computational experience with a primal—dual interior point method for linear programming,”Linear Algebra and its Applications 152 (1991) 191–222.

    Google Scholar 

  5. A. Prékopa, “Dual method for a one-stage stochastic programming problem with random RHS obeying a discrete probability distribution,”Zeitschrift für Operations Research 34 (1990) 441–461.

    Google Scholar 

  6. A. Prékopa and W. Li, “On an optimization problem concerning the stochastic PERT problem,” RUTCOR Research Report 18-92, 1992.

  7. A. Prékopa and J. Long, “New bounds and approximations for the probability distribution of the length of the critical path,” RUTCOR Research Report 16-92, 1992.

  8. S.W. Wallace, “Decomposing the requirement space of a transportation problem into polyhedral cones,”Mathematical Programming Study 28 (1986) 295–317.

    Google Scholar 

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This research was supported by the National Science Foundation, Grant No. DMS-9005159.

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Prékopa, A., Li, W. Solution of and bounding in a linearly constrained optimization problem with convex, polyhedral objective function. Mathematical Programming 70, 1–16 (1995). https://doi.org/10.1007/BF01585925

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  • DOI: https://doi.org/10.1007/BF01585925

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