convexity with respect to cones

A quadratically convergent Newton method for vector optimization

  • L. M. Graña Drummond
  • Benar Fux Svaiter
  • Fernanda M. P. Raupp
    • Categories Convex Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , , ,

    We propose a Newton method for solving smooth unconstrained vector optimization problems under partial orders induced by general closed convex pointed cones. The method extends the one proposed by Fliege, Grana Drummond and Svaiter for multicriteria, which in turn is an extension of the classical Newton method for scalar optimization. The steplength is chosen by … Read more

    On the convergence of the projected gradient method for vector optimization

  • Ellen H. Fukuda
  • L. M. Graña Drummond
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization Tags , , ,

    In 2004, Graña Drummond and Iusem proposed an extension of the projected gradient method for constrained vector optimization problems. In that method, an Armijo-like rule, implemented with a backtracking procedure, was used in order to determine the steplengths. The authors just showed stationarity of all cluster points and, for another version of the algorithm (with … Read more