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 )

Files:

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

Subdirectories:

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

bfgs_mz - several BFGS quasi-Newton codes

Reference:

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