Set approach for set optimization with variable ordering structures. I: Set relations and relationship to vector approach
From MaRDI portal
Publication:504807
DOI10.1007/s10957-016-0992-0zbMath1354.49035OpenAlexW2512666535MaRDI QIDQ504807
Gabriele Eichfelder, Maria Pilecka
Publication date: 17 January 2017
Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10957-016-0992-0
Multi-objective and goal programming (90C29) Nonlinear programming (90C30) Set-valued and variational analysis (49J53) Set-valued maps in general topology (54C60)
Related Items
Solving set-valued optimization problems using a multiobjective approach, A first bibliography on set and vector optimization problems with respect to variable domination structures, Unnamed Item, A Hausdorff-type distance, the Clarke generalized directional derivative and applications in set optimization problems, Characterizations of set relations with respect to variable domination structures via oriented distance function, A Vectorization Scheme for Nonconvex Set Optimization Problems, Approximate elements for set optimization problems with respect to variable domination structures, Characterizations of set order relations and nonlinear scalarizations via generalized oriented distance function in set optimization, Unnamed Item, An order theoretic fixed point theorem with application to multivalued variational inequalities with nonsmooth bifunctions, Set approach for set optimization with variable ordering structures. II: Scalarization approaches, A generalized scalarization method in set optimization with respect to variable domination structures, Unifying local-global type properties in vector optimization, Two Set Scalarizations Based on the Oriented Distance with Variable Ordering Structures: Properties and Application to Set Optimization, Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Vectorization in set optimization
- Variable preference relations: existence of maximal elements
- On optimization problems with set-valued objective maps: existence and optimality
- Necessary nondomination conditions in set and vector optimization with variable ordering structures
- A steepest descent-like method for variable order vector optimization problems
- Characterization of approximate solutions of vector optimization problems with a variable order structure
- Set approach for set optimization with variable ordering structures. II: Scalarization approaches
- New order relations in set optimization
- On solutions of set-valued optimization problems
- Relative Pareto minimizers for multiobjective problems: Existence and optimality conditions
- Variable preference modeling with ideal-symmetric convex cones
- On supremum of a set in a multidimensional space
- Foundations of bilevel programming
- On set-valued optimization problems with variable ordering structure
- \((\Lambda ,C)\)-contingent derivatives of set-valued maps
- Treatment of set order relations by means of a nonlinear scalarization functional: a full characterization
- Optimality conditions for vector optimization problems with variable ordering structures
- Vector Optimization Problems and Their Solution Concepts
- Vector Optimization with Infimum and Supremum
- Supremal points and generalized duality
- On cone convexity of set-valued maps
- Variable Ordering Structures in Vector Optimization
- Set-valued Optimization