differentiability

Lowner’s Operator and Spectral Functions in Euclidean Jordan Algebras

  • Jie Sun
  • Defeng Sun
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

    We study analyticity, differentiability, and semismoothness of Lowner’s operator and spectral functions under the framework of Euclidean Jordan algebras. In particular, we show that many optimization-related classical results in the symmetric matrix space can be generalized within this framework. For example, the metric projection operator over any symmetric cone defined in a Euclidean Jordan algebra … Read more

    Envelope Theorems For Finite Choice Sets

  • Somdeb Lahiri
    • Categories Finance and Economics, Game Theory, Multi-Criteria Optimization Tags , , ,

    This paper is concerned with the study of envelope theorems for finite choice sets. More specifically, we consider the problem of differentiability of the value function arising out of the maximization of a parametrized objective function, when the set of alternatives is non-empty and finite. The parameter is confined to the closed interval [0,1] and … Read more