Abstract
large-scale nonlinear optimization problems. The method is based on
an approach proposed by Gould and Toint (Math. Prog.,
122(1):155-196, 2010) that focused on solving equality constrained
problems. Our method, which is designed to solve problems with both
equality and inequality constraints, achieves global convergence
guarantees by combining a trust-region methodology with a funnel
mechanism. The prominent features of our algorithm are that (i) the
subproblems that define each search direction may be solved
approximately, (ii) criticality measures for feasibility and
optimality aid in determining which subset of computations will be
performed during each iteration, (iii) no merit function or filter is
used, (iv) inexact sequential quadratic optimization steps may be
computed when advantageous, and (v) it may be implemented matrix-free
so that derivative matrices need not be formed or factorized so long
as matrix-vector products with them can be performed.
| Language | English |
|---|---|
| Pages | 73-134 |
| Number of pages | 43 |
| Journal | Mathematical Programming |
| Volume | 161 |
| Issue number | 1 |
| State | Published - Jan 2017 |
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Keywords
- Nonlinear optimization
- numerical methods
- convergence theory
Cite this
}
An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization. / Curtis, Frank; Gould, N. I. M.; Robinson, Daniel; Toint, Ph.
In: Mathematical Programming, Vol. 161, No. 1, 01.2017, p. 73-134.Research output: Contribution to journal › Article
TY - JOUR
T1 - An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization
AU - Curtis,Frank
AU - Gould,N. I. M.
AU - Robinson,Daniel
AU - Toint,Ph
PY - 2017/1
Y1 - 2017/1
N2 - We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math. Prog., 122(1):155-196, 2010) that focused on solving equality constrained problems. Our method, which is designed to solve problems with both equality and inequality constraints, achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism. The prominent features of our algorithm are that (i) the subproblems that define each search direction may be solved approximately, (ii) criticality measures for feasibility and optimality aid in determining which subset of computations will be performed during each iteration, (iii) no merit function or filter is used, (iv) inexact sequential quadratic optimization steps may be computed when advantageous, and (v) it may be implemented matrix-free so that derivative matrices need not be formed or factorized so long as matrix-vector products with them can be performed.
AB - We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math. Prog., 122(1):155-196, 2010) that focused on solving equality constrained problems. Our method, which is designed to solve problems with both equality and inequality constraints, achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism. The prominent features of our algorithm are that (i) the subproblems that define each search direction may be solved approximately, (ii) criticality measures for feasibility and optimality aid in determining which subset of computations will be performed during each iteration, (iii) no merit function or filter is used, (iv) inexact sequential quadratic optimization steps may be computed when advantageous, and (v) it may be implemented matrix-free so that derivative matrices need not be formed or factorized so long as matrix-vector products with them can be performed.
KW - Nonlinear optimization
KW - numerical methods
KW - convergence theory
M3 - Article
VL - 161
SP - 73
EP - 134
JO - Mathematical Programming
T2 - Mathematical Programming
JF - Mathematical Programming
SN - 0025-5610
IS - 1
ER -