| Summary: | This thesis proposes a new active-set method for large-scale nonlinearly con
strained optimization. The method solves a sequence of linear programs to
generate search directions. The typical approach for globalization is based on
damping the search directions with a trust-region constraint; our proposed ap
proach is instead based on using a 2-norm regularization term in the objective.
Numerical evidence is presented which demonstrates scaling inefficiencies
in current sequential linear programming algorithms that use a trust-region
constraint. Specifically, we show that the trust-region constraints in the trustregion
subproblems significantly reduce the warm-start efficiency of these subproblem
solves, and also unnecessarily induce infeasible subproblems. We also
show that the use of a regularized linear programming (RLP) step largely elim
inates these inefficiencies and, additionally, that the dual problem to RLP is
a bound-constrained least-squares problem, which may allow for very efficient
subproblem solves using gradient-projection-type algorithms.
Two new algorithms were implemented and are presented in this thesis,
based on solving sequences of RLPs and trust-region constrained LPs. These
algorithms are used to demonstrate the effectiveness of each type of subproblem,
which we extrapolate onto the effectiveness of an RLP-based algorithm with the
addition of Newton-like steps.
All of the source code needed to reproduce the figures and tables presented
in this thesis is available online at
http: //www.cs.ubc.ca/labs/scl/thesis/lOcrowe/
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