Abstract

We provide Moreau-Rockafellar type theorems for a kind of proper ε-subdifferential of vector-valued mappings. For this aim, we introduce and study a new notion of approximate strong solution of a vector optimization problem, a new strong ε-subdifferential based on this type of approximate strong solutions, and a new regularity condition. Finally, as a consequence of the obtained exact sum rules, the gap between the strong and the proper ε-subdifferentials is provided.

Author information

Contact details are reproduced from the original publication and may be historical.

César Gutiérrez

Dep. de Matemática Aplicada, Universidad de Valladolid, Paseo de Belén 15, Campus Miguel Delibes, 47011 Valladolid, Spain

cesargv@mat.uva.es

Lidia Huerga

Dep. de Matemática Aplicada, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal 12, Ciudad Universitaria, 28040 Madrid, Spain

lhuerga@bec.uned.es

Bienvenido Jiménez

Dep. de Matemática Aplicada, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal 12, Ciudad Universitaria, 28040 Madrid, Spain

bjimenez@ind.uned.es

Vicente Novo

Dep. de Matemática Aplicada, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal 12, Ciudad Universitaria, 28040 Madrid, Spain

vnovo@ind.uned.es

Keywords

  • Vector optimization
  • proper epsilon-efficiency
  • proper epsilon-subdifferential
  • nearly subconvexlikeness
  • strong epsilon-efficiency
  • strong epsilon-subdifferential
  • linear scalarization
  • epsilon-subdifferential

Mathematics Subject Classification

90C48, 90C25, 90C29, 49J52, 49K27

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Suggested citation

C. Gutiérrez, L. Huerga, B. Jiménez, V. Novo. “Proper Approximate Solutions and ε-Subdifferentials in Vector Optimization: Moreau-Rockafellar Type Theorems.” Journal of Convex Analysis 21 (2014), No. 3, 857–886. https://doi.org/10.68381/jca21047

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press LLC.