An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization

                F. Curtis, N. Gould, D. Robinson and Ph. L. Toint 
                Report NAXYS-02-2014             20 February 2014

  We present an interior-point  trust-funnel algorithm for solving large-scale
  nonlinear  optimization  problems.   The  method is  based  on  an  approach
  proposed by Gould and Toint  (Math. Prog., 122(1):155-196, 2010) that
  focused on solving equality constrained  problems.  Our method is similar in
  that it achieves  global convergence guarantees by  combining a trust-region
  methodology with a funnel mechanism,  but has the additional capability that
  it  solves problems  with  both equality  and  inequality constraints.   The
  prominent features of our algorithm are that (i) the subproblems that define
  each search direction may be solved approximately, (ii) criticality measures
  for  feasibility  and   optimality  aid  in  determining   which  subset  of
  computations  will  be  performed  during each  iteration,  (iii)  no  merit
  function or filter  is used, (iv) inexact  sequential quadratic optimization
  steps  may be  utilized when  advantageous, and  (v) it  may be  implemented
  matrix-free so that derivative matrices need  not be formed or factorized so
  long as matrix-vector products with them can be performed.