Erik Alex Papa Quiroz

A NEW BARRIER FOR A CLASS OF SEMIDEFINITE PROBLEMS

  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
    • Categories Semi-definite Programming Tags , , ,

    We introduce a new barrier function to solve a class of Semidefinite Optimization Problems (SOP) with bounded variables. That class is motivated by some (SOP) as the minimization of the sum of the first few eigenvalues of symmetric matrices and graph partitioning problems. We study the primal-dual central path defined by the new barrier and … Read more

    A NEW SELF-CONCORDANT BARRIER FOR THE HYPERCUBE

  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
    • Categories Bound-constrained Optimization, Linear Programming Tags ,

    In this paper we introduce a new barrier function $\sum\limits_{i=1}^n(2x_i-1)[\ln{x_i}-\ln(1-x_i)]$ to solve the following optimization problem: $\min\,\, f(x)$ subject to: $Ax=b;\;\;0\leq x\leq e$. We show that this function is a $(3/2)n$-self-concordant barrier on the hypercube $[0,1]^n$. We prove that the central path is well defined and that under an additional assumption on the objective function, … Read more