A Hausdorff-type distance, a directional derivative of a set-valued map and applications in set optimization
From MaRDI portal
Publication:3177618
DOI10.1080/02331934.2017.1420186zbMath1414.90311OpenAlexW2781767924MaRDI QIDQ3177618
Publication date: 1 August 2018
Published in: Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/02331934.2017.1420186
Multi-objective and goal programming (90C29) Optimality conditions and duality in mathematical programming (90C46)
Related Items (18)
New concepts of directional derivatives for set-valued maps and applications to set optimization ⋮ A Hausdorff-type distance, the Clarke generalized directional derivative and applications in set optimization problems ⋮ A set scalarization function and Dini directional derivatives with applications in set optimization problems ⋮ Lagrange multipliers in convex set optimization with the set and vector criteria ⋮ Ekeland’s variational principle with a scalarization type weighted set order relation ⋮ Optimality and error bound for set optimization with application to uncertain multi-objective programming ⋮ Stability of optimal points with respect to improvement sets ⋮ A set scalarization function based on the oriented distance and relations with other set scalarizations ⋮ Lagrange Multiplier Rules for Weakly Minimal Solutions of Compact-Valued Set Optimization Problems ⋮ Six set scalarizations based on the oriented distance: continuity, convexity and application to convex set optimization ⋮ Six set scalarizations based on the oriented distance: properties and application to set optimization ⋮ Two Set Scalarizations Based on the Oriented Distance with Variable Ordering Structures: Properties and Application to Set Optimization ⋮ Characterization of set relations through extensions of the oriented distance ⋮ A new concept of slope for set-valued maps and applications in set optimization studied with Kuroiwa's set approach ⋮ On Lagrange Multiplier Rules for Set-Valued Optimization Problems in the Sense of Set Criterion ⋮ Existence of Lagrange multipliers for set optimization with application to vector equilibrium problems ⋮ Some characterizations of a nonlinear scalarizing function via oriented distance function ⋮ On Lipschitz continuity of solutions to equilibrium problems via the Hiriart-Urruty oriented distance function
Cites Work
- The Lipschitzianity of convex vector and set-valued functions
- Optimality conditions for set-valued optimisation problems using a modified Demyanov difference
- Directional derivatives in set optimization with the set less order relation
- New order relations in set optimization
- Generalized Newton's method based on graphical derivatives
- Convexity for set-valued maps
- Lagrange multipliers for set-valued optimization problems associated with coderivatives
- A Survey of Set Optimization Problems with Set Solutions
- Set Optimization Meets Variational Inequalities
- Estimates of Error Bounds for Some Sets of Efficient Solutions of a Set-Valued Optimization Problem
- Notes about extended real- and set-valued functions
- Directional derivatives and subdifferentials of set-valued convex functions
- Vector Optimization
- Set-valued optimization in welfare economics
- Difference of compact sets in the sense of demyanov and its application to non-smooth analysis
- On cone convexity of set-valued maps
- Degrees of Efficiency and Degrees of Minimality
- Set-valued analysis
- Existence and density results for proper efficiency in cone compact sets
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: A Hausdorff-type distance, a directional derivative of a set-valued map and applications in set optimization