An Active Set Strategy for Solving Optimization Problems with up to
200,000,000 Nonlinear Constraints
K. Schittkowski: Applied Numerical Mathematics, Vol. 59, 2999-3007 (2009)
We propose a numerical algorithm for solving smooth nonlinear programming
problems with a large number of constraints, but a moderate number of variables.
The active set method proceeds from a given bound m_w for the maximum number of
expected violated constraints, where m_w is a user-provided parameter less than
the total number of constraints. A quadratic programming subproblem is generated
with m_w linear constraints, the so-called working set, which are internally
exchanged from one iterate to the next. Only for active constraints, i.e., a
certain subset of the working set, new gradient values must be computed. The
line search takes the active constraints into account. Numerical results for
some simple academic test problems show that nonlinear programs with up to
200,000,000 nonlinear constraints can be efficiently solved within a few minutes
on a standard PC.
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