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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Veröffentlicht in:European journal of operational research Jg. 205; H. 3; S. 501 - 506
1. Verfasser: MAINGE, Paul-Emile
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 16.09.2010
Elsevier
Elsevier Sequoia S.A
Schriftenreihe:European Journal of Operational Research
Schlagworte:
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
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
ISSN:0377-2217, 1872-6860
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Beschreibung
Zusammenfassung: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.
Bibliographie:SourceType-Scholarly Journals-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2010.01.042