jordan algebra

The solution of Euclidean norm trust region SQP subproblems via second order cone programs, an overview and elementary introduction

  • Florian Jarre
  • Felix Lieder
    • Categories Constrained Nonlinear Optimization, Second-Order Cone Programming Tags , ,

    It is well known that convex SQP subproblems with a Euclidean norm trust region constraint can be reduced to second order cone programs for which the theory of Euclidean Jordan-algebras leads to efficient interior-point algorithms. Here, a brief and self-contained outline of the principles of such an implementation is given. All identities relevant for the … Read more

    Uniform nonsingularity and complementarity problems over symmetric cones

  • Chek Beng Chua
  • Huiling Lin
  • Peng Yi
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    We study the uniform nonsingularity property recently proposed by the authors and present its applications to nonlinear complementarity problems over a symmetric cone. In particular, by addressing theoretical issues such as the existence of Newton directions, the boundedness of iterates and the nonsingularity of B-subdifferentials, we show that the non-interior continuation method proposed by Xin … Read more

    A continuation method for nonlinear complementarity problems over symmetric cone

  • Chek Beng Chua
  • Peng Yi
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    In this paper, we introduce a new P-type condition for nonlinear functions defined over Euclidean Jordan algebras, and study a continuation method for nonlinear complementarity problems over symmetric cones. This new P-type condition represents a new class of nonmonotone nonlinear complementarity problems that can be solved numerically. CitationResearch Report, Division of Mathematical Sciences, School of … Read more

    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