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Computable bounds on parametric solutions of convex problems

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Abstract

We present a new method for computing bounds on parametric solutions of convex problems. The approach is based on a uniform quadratic underestimation of the objective function and a simple technique for the calculation of bounds on the optimal value function.

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References

  1. J.W. Daniel, “Stability of the solution of definite quadratic programs,”Mathematical Programming 5 (1973) 41–53.

    Google Scholar 

  2. A.V. Fiacco, “Computable optimal value bounds and solution vector estimates for general parametric NLP programs,” The George Washington University, Washington, DC, Technical Paper T-451 (1981).

    Google Scholar 

  3. A.V. Fiacco,Introduction to Sensitivity and Stability Analysis in Nonlinear Programming (Academic Press, New York, 1983).

    Google Scholar 

  4. A.V. Fiacco and J. Kyparisis, “Computable parametric bounds for simultaneous large perturbations of thirty parameters in a water pollution abatement GP model. Part II: Refinement of optimal value bounds and parametric solution bounds,” The George Washington University, Washington, DC, Technical Paper Serial T-461, December 1981.

    Google Scholar 

  5. A. Ghaemi, “Computable stability analysis techniques for nonlinear programming: sensitivities, optimal value bounds, and applications,” Doctoral dissertation, School of Engineering and Applied Science, The George Washington University, Washington, DC, 1980.

    Google Scholar 

  6. E. Hansen, “Global optimization using interval analysis—the multi-dimensional case,”Numerische Mathematik 34 (1980) 247–270.

    Google Scholar 

  7. E. Hansen, “Global optimization with data perturbations,”Computers and Operations Research 11 (1984) 97–104.

    Google Scholar 

  8. O.L. Mangasarian and J.B. Rosen, “Inequalities for stochastic nonlinear programming problems,”Operations Research 12 (1964) 143–154.

    Google Scholar 

  9. S.M. Robinson, “Computable error bounds for nonlinear programming,”Mathematical Programming 5 (1973) 235–242.

    Google Scholar 

  10. S.M. Robinson, “Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear programming algorithms,”Mathematical Programming 7 (1974) 1–16.

    Google Scholar 

  11. S.M. Robinson, “An application of error bounds for convex programming in a linear space,”SIAM Journal of Control and Optimization 13 (1975) 271–273.

    Google Scholar 

  12. S.M. Robinson, “Generalized equations and their solutions, Part I: Basic theory,”Mathematical Programming Study 10 (1979) 128–141.

    Google Scholar 

  13. S.M. Robinson, “Strongly regular generalized equations,”Mathematics of Operations Research 5 (1980) 43–62.

    Google Scholar 

  14. M.H. Stern and D.M. Topkis, “Rates of stability in nonlinear programming,”Operations Research 24 (1976) 462–476.

    Google Scholar 

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Research supported by Grant ECS-8619859, National Science Foundation and Contract N00017-86-K-0052, Office of Naval Research.

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Fiacco, A.V., Kyparisis, J. Computable bounds on parametric solutions of convex problems. Mathematical Programming 40, 213–221 (1988). https://doi.org/10.1007/BF01580732

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  • DOI: https://doi.org/10.1007/BF01580732

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