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Variational Analysis of Composite Models with Applications to Continuous Optimization

Author

Listed:
  • Ashkan Mohammadi

    (Department of Mathematics, Wayne State University, Detroit, Michigan 48201)

  • Boris S. Mordukhovich

    (Department of Mathematics, Wayne State University, Detroit, Michigan 48201)

  • M. Ebrahim Sarabi

    (Department of Mathematics, Miami University, Oxford, Ohio 45056)

Abstract

The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate. The underlying theme of our study is a systematical replacement of conventional metric regularity and related requirements by much weaker metric subregulatity ones that lead us to significantly stronger and completely new results of first-order and second-order variational analysis and optimization. In this way, we develop extended calculus rules for first-order and second-order generalized differential constructions while paying the main attention in second-order variational theory to the new and rather large class of fully subamenable compositions. Applications to optimization include deriving enhanced no-gap second-order optimality conditions in constrained composite models, complete characterizations of the uniqueness of Lagrange multipliers, strong metric subregularity of Karush-Kuhn-Tucker systems in parametric optimization, and so on.

Suggested Citation

  • Ashkan Mohammadi & Boris S. Mordukhovich & M. Ebrahim Sarabi, 2022. "Variational Analysis of Composite Models with Applications to Continuous Optimization," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 397-426, February.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:1:p:397-426
    DOI: 10.1287/moor.2020.1074
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    References listed on IDEAS

    as
    1. Helmut Gfrerer & Jiří V. Outrata, 2016. "On Computation of Generalized Derivatives of the Normal-Cone Mapping and Their Applications," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1535-1556, November.
    2. J. J. Ye & X. Y. Ye, 1997. "Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 977-997, November.
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    Cited by:

    1. V. D. Thinh & T. D. Chuong & N. L. H. Anh, 2023. "Second order analysis for robust inclusion systems and applications," Journal of Global Optimization, Springer, vol. 85(1), pages 81-110, January.
    2. Matúš Benko & Patrick Mehlitz, 2024. "Isolated Calmness of Perturbation Mappings and Superlinear Convergence of Newton-Type Methods," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1587-1621, November.
    3. Pham Duy Khanh & Boris S. Mordukhovich & Vo Thanh Phat & Dat Ba Tran, 2023. "Generalized damped Newton algorithms in nonsmooth optimization via second-order subdifferentials," Journal of Global Optimization, Springer, vol. 86(1), pages 93-122, May.
    4. Pham Duy Khanh & Boris Mordukhovich & Vo Thanh Phat, 2023. "A Generalized Newton Method for Subgradient Systems," Mathematics of Operations Research, INFORMS, vol. 48(4), pages 1811-1845, November.

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