Stability and scalarization of weak efficient, efficient and Henig proper efficient sets using generalized quasiconvexities

DOI10.1007/s10957-012-0106-6zbMath1272.90079OpenAlexW1998412108MaRDI QIDQ1935278

C. S. Lalitha, Prashanto Chatterjee

Publication date: 14 February 2013

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-012-0106-6

zbMATH Keywords

stabilityquasiconvexityefficient setconstrained vector optimization problemKuratowski-Painlevé set convergence

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Sensitivity, stability, parametric optimization (90C31)

Related Items (24)

Stability of set-valued optimization problems with naturally quasi-functions ⋮ Convergence Results for Henig Proper Efficient Solution Sets of Vector Optimization Problems ⋮ Convergence of the solution sets for set optimization problems ⋮ Essential stability in set optimization ⋮ Painlevé–Kuratowski convergences of the solution sets for set optimization problems with cone-quasiconnectedness ⋮ Painlevé-Kuratowski convergence of minimal solutions for set-valued optimization problems via improvement sets ⋮ Stability in unified semi-infinite vector optimization ⋮ Unnamed Item ⋮ External and internal stability in set optimization ⋮ Stability and scalarization in vector optimization using improvement sets ⋮ Semicontinuity of the minimal solution set mappings for parametric set-valued vector optimization problems ⋮ Vector optimization using improvement sets in locally convex spaces ⋮ Painlevé-Kuratowski stability of the solution sets to perturbed vector generalized systems ⋮ Parametric vector optimization ⋮ Scalarization of Levitin-Polyak well-posedness in vector optimization using weak efficiency ⋮ Set convergence of non-convex vector optimization problem with variable ordering structure ⋮ Continuity of the efficient solution mapping for vector optimization problems ⋮ Convergence for vector optimization problems with variable ordering structure ⋮ The stability and extended well-posedness of the solution sets for set optimization problems via the Painlevé-Kuratowski convergence ⋮ On Levitin-Polyak well-posedness and stability in set optimization ⋮ Stability and scalarization for a unified vector optimization problem ⋮ Stability of approximating solutions to parametric bilevel vector equilibrium problems and applications ⋮ Stability results for properly quasi convex vector optimization problems ⋮ Painlevé-Kuratowski convergences of the solution sets for vector optimization problems with free disposal sets

Cites Work

• Scalarization of Henig properly efficient points in locally convex spaces
• Convexity and well-posed problems
• Sensitivity analysis of vector equilibrium problems
• A convergence for infinite dimensional vector valued functions
• Extended well-posedness of quasiconvex vector optimization problems
• Optimality conditions via scalarization for a new \(\epsilon \)-efficiency concept in vector optimization problems
• Theory of multiobjective optimization
• Scalarization of vector optimization problems
• Generalized quasiconvexities, cone saddle points, and minimax theorem for vector-valued functions
• Convergence of the efficient sets
• Minimax type theorems for n-valued functions
• Scalarization and stability in vector optimization
• Stability for properly quasiconvex vector optimization problem
• Characterization of solutions of multiobjective optimization problem
• A convergence for vector valued functions
• An Existence Theorem in Vector Optimization
• Stability for convex vector optimization problems
• Stability Results for Ekeland's ε-Variational Principle and Cone Extremal Solutions
• Stability in vector-valued and set-valued optimization

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