Partial inverse of a monotone operator

DOI10.1007/BF01448388zbMath0524.90072OpenAlexW2042532613MaRDI QIDQ585088

Publication date: 1983

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01448388

zbMATH Keywords

accretive operator Hilbert space maximal monotone operator variational problems proximal point algorithm partial inverse convex feasibility problems monotone complementarity problems network equilibrium problems

Mathematics Subject Classification ID

Programming involving graphs or networks (90C35) Convex programming (90C25) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) General equilibrium theory (91B50) Methods of successive quadratic programming type (90C55) Linear accretive operators, dissipative operators, etc. (47B44)

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Cites Work