Abstract
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These extremal principles concern measurable set-valued mappings/multifunctions with values in finite-dimensional spaces and are established in both approximate and exact forms. The obtained principles are instrumental to derive via variational approaches integral representations and upper estimates of regular and limiting normals cones to essential intersections of sets defined by measurable multifunctions, which are in turn crucial for novel applications to stochastic and semi-infinite programming.
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The authors are very grateful to three anonymous referees for their numerous comments and remarks that helped us to essentially improve the original presentation.
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Dedicated to Marco López in honor of his 70th birthday, with great respect.
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Research of the Boris S. Mordukhovich was partly supported by the USA National Science Foundation under Grants DMS-1512846 and DMS-1808978, by the USA Air Force Office of Scientific Research under Grant #15RT04, and by the Australian Research Council under Discovery Project DP-190100555. Pedro Pérez-Aros was partially supported by: CONICYT Grants: Fondecyt Regular 1190110 and Fondecyt Regular 1200283 and Programa Regional Mathamsud 20-Math-08 CODE: MATH190003.
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Mordukhovich, B.S., Pérez-Aros, P. New extremal principles with applications to stochastic and semi-infinite programming. Math. Program. 189, 527–553 (2021). https://doi.org/10.1007/s10107-020-01548-4
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DOI: https://doi.org/10.1007/s10107-020-01548-4
Keywords
- Variational analysis
- Generalized differentiation
- Normal cone calculus
- Stochastic programming
- Semi-infinite programming