A Combined SQP-IPM Algorithm for
Solving Large Scale Nonlinear Optimization ProblemsB. Sachsenberg, K.
Optimization Letters Vol. 9, 1271-1282
We consider a combined IPM-SQP method to solve smooth nonline\-ar optimization
problems, which may possess a large number of variables and a sparse Jacobian
matrix of the constraints. Basically, the algorithm is a sequential quadratic
programming (SQP) method, where the quadratic programming subproblem is solved
by a primal-dual interior point method (IPM). A special feature of the algorithm
is that the quadratic programming subproblem does not need to become exactly
solved. To solve large optimization problems, either a limited-memory BFGS
update to approximate the Hessian of the Lagrangian function is applied or the
user specifies the Hessian by himself. Numerical results are presented for the
306 small and dense Hock-Schittkowski problems, for 13 large semi-linear
elliptic control problems after a suitable discretization, and for 35 examples
of the CUTEr test problem collection with more than 5,000 variables.
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