Lagrange-type Functions in Constrained Non-Convex Optimization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
2003
|
| Schriftenreihe: | Applied Optimization
85 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Lagrange and penalty function methods provide a powerful approach, both as a theoretical tool and a computational vehicle, for the study of constrained optimization problems. However, for a nonconvex constrained optimization problem, the classical Lagrange primal-dual method may fail to find a minimum as a zero duality gap is not always guaranteed. A large penalty parameter is, in general, required for classical quadratic penalty functions in order that minima of penalty problems are a good approximation to those of the original constrained optimization problems. It is well-known that penaity functions with too large parameters cause an obstacle for numerical implementation. Thus the question arises how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimization problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints. Some approaches for such a scheme are studied in this book. One of them is as follows: an unconstrained problem is constructed, where the objective function is a convolution of the objective and constraint functions of the original problem. While a linear convolution leads to a classical Lagrange function, different kinds of nonlinear convolutions lead to interesting generalizations. We shall call functions that appear as a convolution of the objective function and the constraint functions, Lagrange-type functions |
| Beschreibung: | 1 Online-Ressource (XIV, 286 p) |
| ISBN: | 9781441991720 9781461348214 |
| ISSN: | 1384-6485 |
| DOI: | 10.1007/978-1-4419-9172-0 |
Internformat
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| 500 | |a Lagrange and penalty function methods provide a powerful approach, both as a theoretical tool and a computational vehicle, for the study of constrained optimization problems. However, for a nonconvex constrained optimization problem, the classical Lagrange primal-dual method may fail to find a minimum as a zero duality gap is not always guaranteed. A large penalty parameter is, in general, required for classical quadratic penalty functions in order that minima of penalty problems are a good approximation to those of the original constrained optimization problems. It is well-known that penaity functions with too large parameters cause an obstacle for numerical implementation. Thus the question arises how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimization problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints. Some approaches for such a scheme are studied in this book. One of them is as follows: an unconstrained problem is constructed, where the objective function is a convolution of the objective and constraint functions of the original problem. While a linear convolution leads to a classical Lagrange function, different kinds of nonlinear convolutions lead to interesting generalizations. We shall call functions that appear as a convolution of the objective function and the constraint functions, Lagrange-type functions | ||
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Datensatz im Suchindex
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| author | Rubinov, Alexander |
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| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4419-9172-0 |
| format | Electronic eBook |
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| isbn | 9781441991720 9781461348214 |
| issn | 1384-6485 |
| language | English |
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| spelling | Rubinov, Alexander Verfasser aut Lagrange-type Functions in Constrained Non-Convex Optimization by Alexander Rubinov, Xiaoqi Yang Boston, MA Springer US 2003 1 Online-Ressource (XIV, 286 p) txt rdacontent c rdamedia cr rdacarrier Applied Optimization 85 1384-6485 Lagrange and penalty function methods provide a powerful approach, both as a theoretical tool and a computational vehicle, for the study of constrained optimization problems. However, for a nonconvex constrained optimization problem, the classical Lagrange primal-dual method may fail to find a minimum as a zero duality gap is not always guaranteed. A large penalty parameter is, in general, required for classical quadratic penalty functions in order that minima of penalty problems are a good approximation to those of the original constrained optimization problems. It is well-known that penaity functions with too large parameters cause an obstacle for numerical implementation. Thus the question arises how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimization problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints. Some approaches for such a scheme are studied in this book. One of them is as follows: an unconstrained problem is constructed, where the objective function is a convolution of the objective and constraint functions of the original problem. While a linear convolution leads to a classical Lagrange function, different kinds of nonlinear convolutions lead to interesting generalizations. We shall call functions that appear as a convolution of the objective function and the constraint functions, Lagrange-type functions Mathematics Discrete groups Mathematical optimization Optimization Operations Research, Management Science Convex and Discrete Geometry Mathematik Lagrange-Formalismus (DE-588)4316154-6 gnd rswk-swf Lagrange-Funktion (DE-588)4166459-0 gnd rswk-swf Nichtkonvexe Optimierung (DE-588)4309215-9 gnd rswk-swf Lagrange-Funktion (DE-588)4166459-0 s Lagrange-Formalismus (DE-588)4316154-6 s Nichtkonvexe Optimierung (DE-588)4309215-9 s 1\p DE-604 Yang, Xiaoqi Sonstige oth Applied Optimization 85 (DE-604)BV010841718 85 https://doi.org/10.1007/978-1-4419-9172-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rubinov, Alexander Lagrange-type Functions in Constrained Non-Convex Optimization Applied Optimization Mathematics Discrete groups Mathematical optimization Optimization Operations Research, Management Science Convex and Discrete Geometry Mathematik Lagrange-Formalismus (DE-588)4316154-6 gnd Lagrange-Funktion (DE-588)4166459-0 gnd Nichtkonvexe Optimierung (DE-588)4309215-9 gnd |
| subject_GND | (DE-588)4316154-6 (DE-588)4166459-0 (DE-588)4309215-9 |
| title | Lagrange-type Functions in Constrained Non-Convex Optimization |
| title_auth | Lagrange-type Functions in Constrained Non-Convex Optimization |
| title_exact_search | Lagrange-type Functions in Constrained Non-Convex Optimization |
| title_full | Lagrange-type Functions in Constrained Non-Convex Optimization by Alexander Rubinov, Xiaoqi Yang |
| title_fullStr | Lagrange-type Functions in Constrained Non-Convex Optimization by Alexander Rubinov, Xiaoqi Yang |
| title_full_unstemmed | Lagrange-type Functions in Constrained Non-Convex Optimization by Alexander Rubinov, Xiaoqi Yang |
| title_short | Lagrange-type Functions in Constrained Non-Convex Optimization |
| title_sort | lagrange type functions in constrained non convex optimization |
| topic | Mathematics Discrete groups Mathematical optimization Optimization Operations Research, Management Science Convex and Discrete Geometry Mathematik Lagrange-Formalismus (DE-588)4316154-6 gnd Lagrange-Funktion (DE-588)4166459-0 gnd Nichtkonvexe Optimierung (DE-588)4309215-9 gnd |
| topic_facet | Mathematics Discrete groups Mathematical optimization Optimization Operations Research, Management Science Convex and Discrete Geometry Mathematik Lagrange-Formalismus Lagrange-Funktion Nichtkonvexe Optimierung |
| url | https://doi.org/10.1007/978-1-4419-9172-0 |
| volume_link | (DE-604)BV010841718 |
| work_keys_str_mv | AT rubinovalexander lagrangetypefunctionsinconstrainednonconvexoptimization AT yangxiaoqi lagrangetypefunctionsinconstrainednonconvexoptimization |