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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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