Scalarization method for Levitin-Polyak well-posedness of vectorial optimization problems

DOI10.1007/s00186-012-0410-9zbMath1258.49037OpenAlexW2038999174MaRDI QIDQ1935959

Fu-Quan Xia, L. Zhu

Publication date: 20 February 2013

Published in: Mathematical Methods of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00186-012-0410-9

zbMATH Keywords

equivalence relationsnonlinear scalarization functionLevitin-Polyak well-posednessDontchev-Zolezzi type measureFuri-Vignoli type measurescalar optimization problemsvectorial optimization problems

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Optimality conditions for minimax problems (49K35)

Related Items

Levitin–Polyak Well-Posedness of Strong Parametric Vector Quasi-equilibrium Problems, Differential optimization in finite-dimensional spaces, Scalarization of Levitin–Polyak well-posed set optimization problems, Well-posed generalized vector equilibrium problems, Scalarization of Levitin-Polyak well-posedness in vector optimization using weak efficiency, Approximate solutions and Levitin-Polyak well-posedness for set optimization using weak efficiency, Scalarization and well-posedness for set optimization using coradiant sets, Well-posed symmetric vector quasi-equilibrium problems

Cites Work

• Nonconvex separation theorems and some applications in vector optimization
• Well-posed optimization problems
• Well-posedness and scalarization in vector optimization
• On approximate solutions in vector optimization problems via scalarization
• On variational principles, level sets, well-posedness, and \(\epsilon\)-solutions in vector optimization
• Scalarization for pointwise well-posed vectorial problems
• Stability analysis for parametric vector optimization problems
• Pointwise well-posedness of perturbed vector optimization problems in a vector-valued variational principle
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