SciELO - Scientific Electronic Library Online

 
vol.34 issue3OPTIMIZATION WITH LINEAR COMPLEMENTARITY CONSTRAINTSON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATION author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

Share


Pesquisa Operacional

Print version ISSN 0101-7438

Abstract

FUKUDA, Ellen H.  and  DRUMMOND, Luis Mauricio Graña. A SURVEY ON MULTIOBJECTIVE DESCENT METHODS. Pesqui. Oper. [online]. 2014, vol.34, n.3, pp.585-620. ISSN 0101-7438.  http://dx.doi.org/10.1590/0101-7438.2014.034.03.0585.

We present a rigorous and comprehensive survey on extensions to the multicriteria setting of three well-known scalar optimization algorithms. Multiobjective versions of the steepest descent, the projected gradient and the Newton methods are analyzed in detail. At each iteration, the search directions of these methods are computed by solving real-valued optimization problems and, in order to guarantee an adequate objective value decrease, Armijo-like rules are implemented by means of a backtracking procedure. Under standard assumptions, convergence to Pareto (weak Pareto) optima is established. For the Newton method, superlinear convergence is proved and, assuming Lipschitz continuity of the objectives second derivatives, it is shown that the rate is quadratic

Keywords : multiobjective optimization; Newton method; nonlinear optimization; projected gradient method; steepest descent method.

        · text in English     · English ( pdf epdf )