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Robust Solution of Nonconvex Global Optimization Problems

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Abstract

The concept of ɛ-approximate optimal solution as widely used in nonconvex global optimization is not quite adequate, because such a point may correspond to an objective function value far from the true optimal value, while being infeasible. We introduce a concept of essential ɛ-optimal solution, which gives a more appropriate approximate optimal solution, while being stable under small perturbations of the constraints. A general method for finding an essential ɛ-optimal solution in finitely many steps is proposed which can be applied to d.c. programming and monotonic optimization.

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References

  1. C.A. Floudas (2000) Deterministic Global Optimization: Theory, Methods and Applications Kluwer Academic Publishers Dordrecht

    Google Scholar 

  2. R. Horst H. Tuy (1996) Global Optimization: Deterministic Approaches EditionNumber3 Springer-Verlag Berlin

    Google Scholar 

  3. Konno H., Thach P.T., Tuy H. (1997). Optimization on Low Rank Nonconvex Structures, Kluwer Academic Publishers

  4. Sherali, H.D. and Adams, W.P. (1999), A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Peroblems, Kluwer Academic Publishers

  5. Tuy, H. (1995), D.C. optimization: Theory, methods and algorithms. In: Horst, R. and Pardalos, P. (eds.), Handbook of Global Optimization , pp. 149–216. Kluwer Academic Publishers

  6. Tuy, H. (1998), Convex Analysis and Global Optimization , Kluwer Academic Publishers

  7. H. Tuy (2000) ArticleTitleMonotonic optimization: Problems and solution approaches SIAM Journal on Optimization 11 IssueID2 464–494 Occurrence Handle10.1137/S1052623499359828

    Article  Google Scholar 

  8. H. Tuy F. Al-Khayyal P.T. Thach (2004) Monotonic optimization: branch and cut methods, preprint Institute of Mathematics Hanoi

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Authors and Affiliations

  1. Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307, Hanoi, Vietnam

    Hoang Tuy

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  1. Hoang Tuy
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Correspondence to Hoang Tuy.

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Tuy, H. Robust Solution of Nonconvex Global Optimization Problems. J Glob Optim 32, 307–323 (2005). https://doi.org/10.1007/s10898-004-2707-6

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  • DOI: https://doi.org/10.1007/s10898-004-2707-6

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