Michael Zibulevsky

PBM  -  penalty/barrier multiplier algorithm for nonlinear optimization with functional constraints


Problem to solve:

  Minimize     f(x),              x \in R^n

  Subject to:   f_i(x) <= 0,     i=1, … , m


User supported Matlab functions for computing the objective and constraints values and their derivatives

Download Matlab Code: Version 16.05.2012 pbmsdp.m is an universal solver for nonlinear and semidefinite programming. It also includes inner L-BFGS solver in C )



   pbmsdp.m                  - PBM optimization solver for nonlinear and semidefinite programming

   pbm_optionset.m  - set parameters of  PBM solver


Example of use in quadratic programming:

  solve_qp  - main script

  fgh_qp    - compute function, gradient and hessian of the penalty aggregate

  qp_print  - (empty) user function for printing results



 minFunc -  Limited memory BFGS  of Mark Schmidt with some updates (minFunc_mz)

 bfgs_mz -  several BFGS quasi-Newton codes



Ben-Tal, A. and Zibulevsky, M. (1997). ``Penalty/Barrier Multiplier Methods for Convex Programming Problems", SIAM Journal on Optimization v. 7 # 2, pp. 347-366,


                                    Haifa,   2009 - 2011