# An External Active-Set Strategy for Solving Optimal Control Problems

### Elijah Polak, Hoam Chung and S. Shankar Sastry

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2007-90

July 16, 2007

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2007/EECS-2007-90.pdf

We present a new, {\em external}, active constraints set strategy for solving nonlinear programming problems with a large number of inequality constraints that arise in the process of discretizing continuous-time optimal control problems with state-space constraints. This strategy constructs a sequence of inequality constrained nonlinear programming problems, containing a progressively larger subset of the constraints in the original problem, and submits them to a nonlinear programming solver for a fixed number of iterations. We prove that this scheme computes a solution of the original problem and show by means of numerical experiments that this strategy results in reductions in computing time ranging from a factor of 6 to a factor of over 100.

BibTeX citation:

@techreport{Polak:EECS-2007-90, Author = {Polak, Elijah and Chung, Hoam and Sastry, S. Shankar}, Title = {An External Active-Set Strategy for Solving Optimal Control Problems}, Institution = {EECS Department, University of California, Berkeley}, Year = {2007}, Month = {Jul}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2007/EECS-2007-90.html}, Number = {UCB/EECS-2007-90}, Abstract = {We present a new, {\em external}, active constraints set strategy for solving nonlinear programming problems with a large number of inequality constraints that arise in the process of discretizing continuous-time optimal control problems with state-space constraints. This strategy constructs a sequence of inequality constrained nonlinear programming problems, containing a progressively larger subset of the constraints in the original problem, and submits them to a nonlinear programming solver for a fixed number of iterations. We prove that this scheme computes a solution of the original problem and show by means of numerical experiments that this strategy results in reductions in computing time ranging from a factor of 6 to a factor of over 100.} }

EndNote citation:

%0 Report %A Polak, Elijah %A Chung, Hoam %A Sastry, S. Shankar %T An External Active-Set Strategy for Solving Optimal Control Problems %I EECS Department, University of California, Berkeley %D 2007 %8 July 16 %@ UCB/EECS-2007-90 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2007/EECS-2007-90.html %F Polak:EECS-2007-90