Projected subgradient techniques and viscosity methods for optimization with variational inequality constraints
In this paper, we propose an easily implementable algorithm in Hilbert spaces for solving some classical monotone variational inequality problem over the set of solutions of mixed variational inequalities. The proposed method combines two strategies: projected subgradient techniques and viscosity-ty...
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| Vydané v: | European journal of operational research Ročník 205; číslo 3; s. 501 - 506 |
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| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Amsterdam
Elsevier B.V
16.09.2010
Elsevier Elsevier Sequoia S.A |
| Edícia: | European Journal of Operational Research |
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| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | In this paper, we propose an easily implementable algorithm in Hilbert spaces for solving some classical monotone variational inequality problem over the set of solutions of mixed variational inequalities. The proposed method combines two strategies: projected subgradient techniques and viscosity-type approximations. The involved stepsizes are controlled and a strong convergence theorem is established under very classical assumptions. Our algorithm can be applied for instance to some mathematical programs with complementarity constraints. |
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| AbstractList | In this paper, we propose an easily implementable algorithm in Hilbert spaces for solving some classical monotone variational inequality problem over the set of solutions of mixed variational inequalities. The proposed method combines two strategies: projected subgradient techniques and viscosity-type approximations. The involved stepsizes are controlled and a strong convergence theorem is established under very classical assumptions. Our algorithm can be applied for instance to some mathematical programs with complementarity constraints. [PUBLICATION ABSTRACT] In this paper, we propose an easily implementable algorithm in Hilbert spaces for solving some classical monotone variational inequality problem over the set of solutions of mixed variational inequalities. The proposed method combines two strategies: projected subgradient techniques and viscosity-type approximations. The involved stepsizes are controlled and a strong convergence theorem is established under very classical assumptions. Our algorithm can be applied for instance to some mathematical programs with complementarity constraints. |
| Author | Maingé, Paul-Emile |
| Author_xml | – sequence: 1 givenname: Paul-Emile surname: MAINGE fullname: MAINGE, Paul-Emile organization: CEREGMIA, Université des Antilles-Guyane, Département Scientifique Interfacultaire, Campus de Schoelcher, 97233, Martinique |
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| Keywords | Mixed variational inequality Complementarity constraints Viscosity method Paramonotone operator Projected subgradient method Nonsmooth optimization Hierarchical problem Viscosity Strong convergence Subgradient optimization Complementarity problem Mixed method Nonsmooth analysis Variational inequality Inequality constraint Hilbert space Numerical convergence Mathematical programming |
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| SubjectTerms | Algorithms Applied sciences Approximation Calculus of variations and optimal control Complementarity constraints Convergence Exact sciences and technology Hierarchical problem Hierarchical problem Projected subgradient method Nonsmooth optimization Viscosity method Paramonotone operator Mixed variational inequality Complementarity constraints Inequalities Mathematical analysis Mathematical programming Mathematics Mixed variational inequality Nonsmooth optimization Operational research Operational research and scientific management Operational research. Management science Optimization Optimization algorithms Optimization and Control Paramonotone operator Projected subgradient method Sciences and techniques of general use Strategy Studies Vector space Viscosity Viscosity method |
| Title | Projected subgradient techniques and viscosity methods for optimization with variational inequality constraints |
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