Solving Lagrangian variational inequalities with applications to stochastic programming
Lagrangian variational inequalities feature both primal and dual elements in expressing first-order conditions for optimality in a wide variety of settings where “multipliers” in a very general sense need to be brought in. Their stochastic version relates to problems of stochastic programming and co...
| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
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SPRINGER HEIDELBERG
2020
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| Online Access: | http://hdl.handle.net/20.500.11937/91433 |
| _version_ | 1848765519279161344 |
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| author | Rockafellar, R.T. Sun, Jie |
| author_facet | Rockafellar, R.T. Sun, Jie |
| author_sort | Rockafellar, R.T. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Lagrangian variational inequalities feature both primal and dual elements in expressing first-order conditions for optimality in a wide variety of settings where “multipliers” in a very general sense need to be brought in. Their stochastic version relates to problems of stochastic programming and covers not only classical formats with inequality constraints but also composite models with nonsmooth objectives. The progressive hedging algorithm, as a means of solving stochastic programming problems, has however focused so far only on optimality conditions that correspond to variational inequalities in primal variables alone. Here that limitation is removed by appealing to a recent extension of progressive hedging to multistage stochastic variational inequalities in general. |
| first_indexed | 2025-11-14T11:36:32Z |
| format | Journal Article |
| id | curtin-20.500.11937-91433 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:36:32Z |
| publishDate | 2020 |
| publisher | SPRINGER HEIDELBERG |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-914332023-04-20T06:12:53Z Solving Lagrangian variational inequalities with applications to stochastic programming Rockafellar, R.T. Sun, Jie Science & Technology Technology Physical Sciences Computer Science, Software Engineering Operations Research & Management Science Mathematics, Applied Computer Science Mathematics Stochastic variational inequality problems Stochastic programming problems Lagrangian variational inequalities Lagrange multipliers Progressive hedging algorithm Proximal point algorithm Composite optimization Lagrangian variational inequalities feature both primal and dual elements in expressing first-order conditions for optimality in a wide variety of settings where “multipliers” in a very general sense need to be brought in. Their stochastic version relates to problems of stochastic programming and covers not only classical formats with inequality constraints but also composite models with nonsmooth objectives. The progressive hedging algorithm, as a means of solving stochastic programming problems, has however focused so far only on optimality conditions that correspond to variational inequalities in primal variables alone. Here that limitation is removed by appealing to a recent extension of progressive hedging to multistage stochastic variational inequalities in general. 2020 Journal Article http://hdl.handle.net/20.500.11937/91433 10.1007/s10107-019-01458-0 English SPRINGER HEIDELBERG fulltext |
| spellingShingle | Science & Technology Technology Physical Sciences Computer Science, Software Engineering Operations Research & Management Science Mathematics, Applied Computer Science Mathematics Stochastic variational inequality problems Stochastic programming problems Lagrangian variational inequalities Lagrange multipliers Progressive hedging algorithm Proximal point algorithm Composite optimization Rockafellar, R.T. Sun, Jie Solving Lagrangian variational inequalities with applications to stochastic programming |
| title | Solving Lagrangian variational inequalities with applications to stochastic programming |
| title_full | Solving Lagrangian variational inequalities with applications to stochastic programming |
| title_fullStr | Solving Lagrangian variational inequalities with applications to stochastic programming |
| title_full_unstemmed | Solving Lagrangian variational inequalities with applications to stochastic programming |
| title_short | Solving Lagrangian variational inequalities with applications to stochastic programming |
| title_sort | solving lagrangian variational inequalities with applications to stochastic programming |
| topic | Science & Technology Technology Physical Sciences Computer Science, Software Engineering Operations Research & Management Science Mathematics, Applied Computer Science Mathematics Stochastic variational inequality problems Stochastic programming problems Lagrangian variational inequalities Lagrange multipliers Progressive hedging algorithm Proximal point algorithm Composite optimization |
| url | http://hdl.handle.net/20.500.11937/91433 |