Orizon Pereira Ferreira

Convex- and Monotone- Transformable Mathematical Programming Problems and a Proximal-Like Point Method

  • João Xavier da Cruz Neto
  • Orizon Pereira Ferreira
  • L. R. Lucambio Pérez
  • S. Z. Nemeth
    • Categories Constrained Nonlinear Optimization, Generalized Convexity/Monoticity, Global Optimization Theory Tags , ,

    The problem of finding singularities of monotone vectors fields on Hadamard manifolds will be considered and solved by extending the well-known proximal point algorithm. For monotone vector fields the algorithm will generate a well defined sequence, and for monotone vector fields with singularities it will converge to a singularity. It will be also shown how … Read more

    Asymptotic behavior of the central path for a special class of degenerate SDP problems

  • João Xavier da Cruz Neto
  • Orizon Pereira Ferreira
  • Renato D.C. Monteiro
    • Categories Semi-definite Programming Tags , , , ,

    This paper studies the asymptotic behavior of the central path $(X(\nu),S(\nu),y(\nu))$ as $\nu \downarrow 0$ for a class of degenerate semidefinite programming (SDP) problems, namely those that do not have strictly complementary primal-dual optimal solutions and whose “degenerate diagonal blocks” $X_{\cT}(\nu)$ and $S_{\cT}(\nu)$ of the central path are assumed to satisfy $\max\{ \|X_{\cT}(\nu)\|, \|S_{\cT}(\nu)\| \} … Read more