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Variational Convexity of Functions in Banach Spaces

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Functional Analysis and Continuous Optimization (IMFACO 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 424))

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Abstract

This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and applied to continuous optimization problems in finite-dimensional spaces. Variational convexity in infinite-dimensional spaces, which is studied here for the first time, is significantly more involved and requires the usage of powerful tools of geometric functional analysis together with variational analysis and generalized differentiation in Banach spaces.

Vu Vinh Huy Khoa and Vo Thanh Phat—Research of this author was partly supported by the US National Science Foundation under grants DMS-1808978 and DMS-2204519.

Boris S. Mordukhovich—Research of this author was partly supported by the US National Science Foundation under grants DMS-1808978 and DMS-2204519, and by the Australian Research Council under Discovery Project DP-190100555.

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Author information

Authors and Affiliations

  1. Member of the Group of Analysis and Applied Mathematics, Department of Mathematics, Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam

    Pham Duy Khanh

  2. Department of Mathematics, Wayne State University, Detroit, Michigan, USA

    Vu Vinh Huy Khoa, Boris S. Mordukhovich & Vo Thanh Phat

Authors
  1. Pham Duy Khanh
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  2. Vu Vinh Huy Khoa
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  3. Boris S. Mordukhovich
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  4. Vo Thanh Phat
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Corresponding author

Correspondence to Boris S. Mordukhovich .

Editor information

Editors and Affiliations

  1. Center of Operations Research, Miguel Hernández University of Elche, Elche, Alicante, Spain

    José M. Amigó

  2. Center of Operations Research, Miguel Hernández University of Elche, Elche, Alicante, Spain

    María J. Cánovas

  3. Department of Mathematics, Alicante University, San Vicente del Raspeig, Alicante, Spain

    Marco A. López-Cerdá

  4. Institute for Pure and Applied Mathematics (IUMPA), Polytechnic University of Valencia, Valencia, Spain

    Manuel López-Pellicer

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Khanh, P.D., Khoa, V.V.H., Mordukhovich, B.S., Phat, V.T. (2023). Variational Convexity of Functions in Banach Spaces. In: Amigó, J.M., Cánovas, M.J., López-Cerdá, M.A., López-Pellicer, M. (eds) Functional Analysis and Continuous Optimization. IMFACO 2022. Springer Proceedings in Mathematics & Statistics, vol 424. Springer, Cham. https://doi.org/10.1007/978-3-031-30014-1_11

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