BibTex format
@unpublished{Neuenhofen:2018,
author = {Neuenhofen, MP and Kerrigan, EC},
publisher = {arXiv},
title = {Dynamic optimization with convergence guarantees},
url = {http://arxiv.org/abs/1810.04059v1},
year = {2018}
}
Publications
Citation
RIS format (EndNote, RefMan)
TY - UNPB
AB - We present a novel direct transcription method to solve optimization problemssubject to nonlinear differential and inequality constraints. In order toprovide numerical convergence guarantees, it is sufficient for the functionsthat define the problem to satisfy boundedness and Lipschitz conditions. Ourassumptions are the most general to date; we do not require uniqueness,differentiability or constraint qualifications to hold and we avoid the use ofLagrange multipliers. Our approach differs fundamentally from state-of-the-artmethods based on collocation. We follow a least-squares approach to findingapproximate solutions to the differential equations. The objective is augmentedwith the integral of a quadratic penalty on the differential equation residualand a logarithmic barrier for the inequality constraints, as well as aquadratic penalty on the point constraint residual. The resulting unconstrainedinfinite-dimensional optimization problem is discretized using finite elements,while integrals are replaced by quadrature approximations if they cannot beevaluated analytically. Order of convergence results are derived, even ifcomponents of solutions are discontinuous.
AU - Neuenhofen,MP
AU - Kerrigan,EC
PB - arXiv
PY - 2018///
TI - Dynamic optimization with convergence guarantees
UR - http://arxiv.org/abs/1810.04059v1
UR - http://hdl.handle.net/10044/1/83261
ER -