On the Intrinsic Core of Convex Cones in Real Linear Spaces

DOI10.1137/19M1283148zbMath1481.90253OpenAlexW3160355202MaRDI QIDQ4989934

Christian Günther, Christiane Tammer, A. P. Farajzadeh, Bahareh Khazayel

Publication date: 27 May 2021

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1283148

zbMATH Keywords

vector optimizationconvex conelinear spacePareto efficiencyseparation theoremintrinsic corelinearity spacerelative algebraic interior

Mathematics Subject Classification ID

Convex programming (90C25) Multi-objective and goal programming (90C29) Ordered topological linear spaces, vector lattices (46A40) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20)

Related Items (7)

Levitin-Polyak well-posedness for vector optimization problems in linear spaces ⋮ Fenchel–Rockafellar theorem in infinite dimensions via generalized relative interiors ⋮ Vector optimization w.r.t. relatively solid convex cones in real linear spaces ⋮ R-convexity in R-vector spaces ⋮ A Vectorization Scheme for Nonconvex Set Optimization Problems ⋮ Nonlinear Cone Separation Theorems in Real Topological Linear Spaces ⋮ The intrinsic core and minimal faces of convex sets in general vector spaces

Cites Work

• Proper efficiency in vector optimization on real linear spaces.
• Relative Pareto minimizers for multiobjective problems: Existence and optimality conditions
• Quasi-relative interior-type constraint qualifications ensuring strong Lagrange duality for optimization problems with cone and affine constraints
• Partially finite convex programming. I: Quasi relative interiors and duality theory
• Weak efficiency in vector optimization using a closure of algebraic type under cone-convexlikeness.
• Notions of relative interior in Banach spaces
• Efficient and weak efficient points in vector optimization with generalized cone convexity
• Unifying local-global type properties in vector optimization
• On relatively solid convex cones in real linear spaces
• Explicitly quasiconvex set-valued optimization
• On the use of the quasi-relative interior in optimization
• Vector Optimization
• Duality in Vector Optimization
• A comparison of constraint qualifications in infinite-dimensional convex programming revisited
• Variational Analysis and Applications
• Regularized nonlinear scalarization for vector optimization problems with PDE-constraints
• Set-valued Optimization
• Vector duality for convex vector optimization problems by means of the quasi-interior of the ordering cone
• Convex Analysis
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