Applied Mathematics and Optimization

, Volume 11, Issue 1, pp 43–56 | Cite as

Generalized Hessian matrix and second-order optimality conditions for problems withC1,1 data

  • Jean-Baptiste Hiriart-Urruty
  • Jean-Jacques Strodiot
  • V. Hien Nguyen


In this paper, we present a generalization of the Hessian matrix toC1,1 functions, i.e., to functions whose gradient mapping is locally Lipschitz. This type of function arises quite naturally in nonlinear analysis and optimization. First the properties of the generalized Hessian matrix are investigated and then some calculus rules are given. In particular, a second-order Taylor expansion of aC1,1 function is derived. This allows us to get second-order optimality conditions for nonlinearly constrained mathematical programming problems withC1,1 data.


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Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  • Jean-Baptiste Hiriart-Urruty
    • 1
  • Jean-Jacques Strodiot
    • 2
  • V. Hien Nguyen
    • 2
  1. 1.UER Mathématiques, Informatique, GestionUniversité Paul Sabatier (Toulouse III)ToulouseFrance
  2. 2.Département de MathématiqueFacultés Universitaires de NamurNamurBelgium

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