## Michael Zibulevsky

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

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## 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 )

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**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,

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*
Haifa, 2009 - 2011*