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Global search perspectives for multiobjective optimization

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  • Alberto Lovison

Abstract

Extending the notion of global search to multiobjective optimization is far than straightforward, mainly for the reason that one almost always has to deal with infinite Pareto optima and correspondingly infinite optimal values. Adopting Stephen Smale’s global analysis framework, we highlight the geometrical features of the set of Pareto optima and we are led to consistent notions of global convergence. We formulate then a multiobjective version of a celebrated result by Stephens and Baritompa, about the necessity of generating everywhere dense sample sequences, and describe a globally convergent algorithm in case the Lipschitz constant of the determinant of the Jacobian is known. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Alberto Lovison, 2013. "Global search perspectives for multiobjective optimization," Journal of Global Optimization, Springer, vol. 57(2), pages 385-398, October.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:2:p:385-398
    DOI: 10.1007/s10898-012-9943-y
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    References listed on IDEAS

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    1. E. Miglierina & E. Molho & M. Rocca, 2008. "Critical Points Index for Vector Functions and Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 479-496, September.
    2. C. Hillermeier, 2001. "Generalized Homotopy Approach to Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 557-583, September.
    3. C. P. Stephens & W. Baritompa, 1998. "Global Optimization Requires Global Information," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 575-588, March.
    4. Wan, Yieh-Hei, 1975. "On local Pareto optima," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 35-42, March.
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    1. Benjamin Martin & Alexandre Goldsztejn & Laurent Granvilliers & Christophe Jermann, 2016. "On continuation methods for non-linear bi-objective optimization: towards a certified interval-based approach," Journal of Global Optimization, Springer, vol. 64(1), pages 3-16, January.
    2. Markus Hartikainen & Alberto Lovison, 2015. "PAINT–SiCon: constructing consistent parametric representations of Pareto sets in nonconvex multiobjective optimization," Journal of Global Optimization, Springer, vol. 62(2), pages 243-261, June.
    3. Alberto Lovison & Kaisa Miettinen, 2021. "On the Extension of the DIRECT Algorithm to Multiple Objectives," Journal of Global Optimization, Springer, vol. 79(2), pages 387-412, February.
    4. Kalyan Shankar Bhattacharjee & Hemant Kumar Singh & Tapabrata Ray, 2017. "An approach to generate comprehensive piecewise linear interpolation of pareto outcomes to aid decision making," Journal of Global Optimization, Springer, vol. 68(1), pages 71-93, May.

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