Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/on-the-use-of-piecewise-linear-models-in-nonlinear-programming-h69rBqxmv8
References (28)
-
J. Morales, J. Nocedal, Yuchen Wu (2012)
A sequential quadratic programming algorithm with an additional equality constrained phaseIma Journal of Numerical Analysis, 32
-
P. Gill, W. Murray, M. Saunders (2002)
SNOPT: An SQP Algorithm for Large-Scale Constrained OptimizationSIAM Rev., 47
-
R. Byrd, N. Gould, J. Nocedal, R. Waltz (2004)
An algorithm for nonlinear optimization using linear programming and equality constrained subproblemsMathematical Programming, 100
-
A.R. Conn, N.I.M. Gould, Ph. Toint (2000)
Trust-Region Methods MPS-SIAM Series on Optimization -
R. Byrd, Gabriel López-Calva, J. Nocedal (2012)
A line search exact penalty method using steering rulesMathematical Programming, 133
-
Lifeng Chen, D. Goldfarb (2011)
An interior-point piecewise linear penalty method for nonlinear programmingMathematical Programming, 128
-
R. Bartels, A. Conn, J. Sinclair (1978)
Minimization Techniques for Piecewise Differentiable Functions: The l_1 Solution to an Overdetermined Linear SystemSIAM Journal on Numerical Analysis, 15
-
R. Byrd, R. Waltz (2011)
An active-set algorithm for nonlinear programming using parametric linear programmingOptimization Methods and Software, 26
-
J. Nocedal, S.J. Wright (1999)
Numerical Optimization. Springer Series in Operations Research -
W. Candler, G. Hadley (1965)
Nonlinear and Dynamic Programming, 128
-
M.R. Celis, J.E. Dennis, R.A. Tapia (1985)
Numerical Optimization 1984 -
P.E. Gill, W. Murray, M.A. Saunders (2002)
SNOPT: an SQP algorithm for large-scale constrained optimizationSIAM J. Optim., 12
-
(2011)
On the Implementation of a Method for Nonlinear Programming Based on Piecewise Linear Models -
E. Allgower, K. Georg (2000)
Piecewise linear methods for nonlinear equations and optimizationJournal of Computational and Applied Mathematics, 124
-
R. Byrd, J. Nocedal, Bobby Schnabel (1994)
Representations of quasi-Newton matrices and their use in limited memory methodsMathematical Programming, 63
-
J. Nocedal, Stephen Wright (2018)
Numerical Optimization -
M. Powell, Ya-xiang Yuan (1990)
A trust region algorithm for equality constrained optimizationMathematical Programming, 49
-
G. Dantzig (1956)
RECENT ADVANCES IN LINEAR PROGRAMMINGManagement Science, 2
-
C. Oberlin, S.J. Wright (2006)
Active constraint identification in nonlinear programmingSIAM J. Optim., 17
-
N. Gould, Daniel Robinson (2010)
A Second Derivative SQP Method: Global ConvergenceSIAM J. Optim., 20
-
C. Chin, R. Fletcher (2003)
On the global convergence of an SLP–filter algorithm that takes EQP stepsMathematical Programming, 96
-
M. Friedlander, N. Gould, S. Leyffer, T. Munson (2007)
A Filter Active-Set Trust-Region Method -
R. Fletcher, E. Maza (1989)
Nonlinear programming and nonsmooth optimization by successive linear programmingMathematical Programming, 43
-
M. Celis, J. Dennis, R. Tapia (1984)
A trust region strategy for nonlinear equality constrained op-timization -
R. Fletcher, S. Leyffer (2002)
Nonlinear programming without a penalty functionMathematical Programming, 91
-
J. Nocedal, R. Waltz (2002)
Algorithms for large-scale nonlinear optimization -
(2008)
Steering exact penalty methods -
R. Byrd, N. Gould, J. Nocedal, R. Waltz (2005)
On the Convergence of Successive Linear-Quadratic Programming AlgorithmsSIAM J. Optim., 16
- Publisher
- Springer Journals
- Copyright
- Copyright © 2011 by Springer and Mathematical Optimization Society
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Mathematics of Computing; Numerical Analysis; Combinatorics; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics
- ISSN
- 0025-5610
- eISSN
- 1436-4646
- DOI
- 10.1007/s10107-011-0492-9
- Publisher site
- See Article on Publisher Site
Abstract
This paper presents an active-set algorithm for large-scale optimization that occupies the middle ground between sequential quadratic programming and sequential linear-quadratic programming methods. It consists of two phases. The algorithm first minimizes a piecewise linear approximation of the Lagrangian, subject to a linearization of the constraints, to determine a working set. Then, an equality constrained subproblem based on this working set and using second derivative information is solved in order to promote fast convergence. A study of the local and global convergence properties of the algorithm highlights the importance of the placement of the interpolation points that determine the piecewise linear model of the Lagrangian.
Journal
Mathematical Programming – Springer Journals
Published: Oct 12, 2011