On the public citation graph

Existence and Lagrangian duality for maximizations of set-valued functions

https://doi.org/10.1007/bf00940198
0 signed · 146 inferred · view as graph

Inferred edges come from two machine sources: sweeps of open repository metadata (mostly SSRN and Zenodo), and a bulk OpenAlex citation snapshot. Every row below is labelled with the one it came from. Neither is a complete citation index — absence here is not evidence of absence.

Is this your work? Sign in with ORCID and put your name on the claims that are yours.
Claim with ORCID
Reference health. See whether every reference in this work resolves to a known work and none has been retracted — and get a dated CiteStamped badge you can embed.
See reference health

What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/bf00933437openalex-snapshot
Duality theory in multiobjective programming
inferredcites →https://doi.org/10.1007/bf00934115openalex-snapshot
An existence result for maximizations with respect to cones
inferredcites →https://doi.org/10.1007/bf01584336openalex-snapshot
Multivalued convexity and optimization: A unified approach to inequality and equality constraints
inferredcites →https://doi.org/10.1007/bfb0120850openalex-snapshot
Generalized equations and their solutions, Part I: Basic theory
inferredcites →https://doi.org/10.1016/0022-247x(81)90188-8openalex-snapshot
Duality theory for maximizations with respect to cones
inferredcites →https://doi.org/10.1049/sqj.1970.0088openalex-snapshot
Optimization by Vector Space Methods
inferredcites →https://doi.org/10.1137/1.9781611971309openalex-snapshot
Optimization and Nonsmooth Analysis
inferredcites →https://doi.org/10.1137/1015073openalex-snapshot
Point-to-Set Maps in Mathematical Programming
inferredcites →https://doi.org/10.1287/moor.7.1.95openalex-snapshot
A Duality Theorem in Multiobjective Nonlinear Programming
inferredcites →https://doi.org/10.2307/1909424openalex-snapshot
Nonlinear Programming: A Unified Approach
inferredcites →https://doi.org/10.2307/2343701openalex-snapshot
Nonlinear Programming: A Unified Approach.

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1006/jmaa.1996.0251openalex-snapshot
Duality for Vector Optimization of Set-Valued Functions
inferred← citeshttps://doi.org/10.1006/jmaa.1997.5568openalex-snapshot
Lagrangian Multipliers, Saddle Points, and Duality in Vector Optimization of Set-Valued Maps
inferred← citeshttps://doi.org/10.1006/jmaa.1997.5599openalex-snapshot
Lagrangian Duality for Preinvex Set-Valued Functions
inferred← citeshttps://doi.org/10.1006/jmaa.1997.5644openalex-snapshot
Optimality Conditions for Multiobjective Programming with Generalized (I,ρ,θ)-Convex Set Functions
inferred← citeshttps://doi.org/10.1006/jmaa.1997.5676openalex-snapshot
Conjugate Duality in Set-Valued Vector Optimization
inferred← citeshttps://doi.org/10.1006/jmaa.1998.6187openalex-snapshot
Duality for a Minimax Programming Problem Containingn-Set Functions
inferred← citeshttps://doi.org/10.1006/jmaa.1999.6425openalex-snapshot
Lagrange Duality in Multiobjective Fractional Programming Problems with n-Set Functions
inferred← citeshttps://doi.org/10.1006/jmaa.2000.6715openalex-snapshot
On Minimax Fractional Programming of Generalized Convex Set Functions
inferred← citeshttps://doi.org/10.1007/0-306-48107-3_1openalex-snapshot
Theory of Vector Optimization
inferred← citeshttps://doi.org/10.1007/0-306-48332-7_460openalex-snapshot
Set-Valued Optimization
inferred← citeshttps://doi.org/10.1007/3-540-28258-0_4openalex-snapshot
Benson Proper Efficiency in Set-Valued Optimization on Real Linear Spaces
inferred← citeshttps://doi.org/10.1007/978-0-387-74759-0_600openalex-snapshot
Set-valued Optimization
inferred← citeshttps://doi.org/10.1007/978-3-322-81539-2_3openalex-snapshot
Grundlagen der Mengenoptimierung
inferred← citeshttps://doi.org/10.1007/978-3-642-51682-5_28openalex-snapshot
Fenchel Duality in Vector Optimization
inferred← citeshttps://doi.org/10.1007/978-3-642-54265-7_8openalex-snapshot
Duality
inferred← citeshttps://doi.org/10.1007/978-3-662-48670-2_3openalex-snapshot
Set Optimization—A Rather Short Introduction
inferred← citeshttps://doi.org/10.1007/978-981-16-1819-2_6openalex-snapshot
Set Order Relations, Set Optimization, and Ekeland’s Variational Principle
inferred← citeshttps://doi.org/10.1007/978-981-97-8907-8_5openalex-snapshot
Results on Existence of l-Minimal and u-Minimal Solutions in Set-Valued Optimization: A Brief Survey
inferred← citeshttps://doi.org/10.1007/978-981-97-8907-8_6openalex-snapshot
Scalarization for Set Optimization in Vector Spaces
inferred← citeshttps://doi.org/10.1007/bf00939767openalex-snapshot
Optimality conditions for maximizations of set-valued functions
inferred← citeshttps://doi.org/10.1007/bf01098361openalex-snapshot
On the existence of efficient points in locally convex spaces
inferred← citeshttps://doi.org/10.1007/bf01194174openalex-snapshot
A note on connectivity of efficient solution sets
inferred← citeshttps://doi.org/10.1007/bf01217689openalex-snapshot
Upper-semi-continuity and cone-concavity of multi-valued vector functions in a duality theory for vector optimization
inferred← citeshttps://doi.org/10.1007/bf01594928openalex-snapshot
Contingent derivatives of set-valued maps and applications to vector optimization
inferred← citeshttps://doi.org/10.1007/bf02191762openalex-snapshot
Lagrange Multipliers and saddle points in multiobjective programming
inferred← citeshttps://doi.org/10.1007/bf02191763openalex-snapshot
Connectedness of efficient solution sets for set-valued maps in normed spaces
inferred← citeshttps://doi.org/10.1007/bf02192246openalex-snapshot
An optimization result for set-valued mappings and a stability property in vector problems with constraints
inferred← citeshttps://doi.org/10.1007/bf02192940openalex-snapshot
Extension of the Zorn lemma to general nontransitive binary relations
inferred← citeshttps://doi.org/10.1007/bf03398587openalex-snapshot
Theorems of the Alternative for Multifunctions
inferred← citeshttps://doi.org/10.1007/bf03399199openalex-snapshot
A Note on Quasiconvex Set-Valued Maps
inferred← citeshttps://doi.org/10.1007/s00186-005-0007-7openalex-snapshot
ɛ-Subdifferentials of Set-valued Maps and ɛ-Weak Pareto Optimality for Multiobjective Optimization
inferred← citeshttps://doi.org/10.1007/s00186-015-0509-xopenalex-snapshot
Pointwise well-posedness and scalarization in set optimization
inferred← citeshttps://doi.org/10.1007/s001860050026openalex-snapshot
Characterizations of super efficiency in cone-convexlike vector optimization with set-valued maps
inferred← citeshttps://doi.org/10.1007/s001860050027openalex-snapshot
A generalization of Fenchel duality in set-valued vector optimization
inferred← citeshttps://doi.org/10.1007/s10114-011-0294-2openalex-snapshot
On Ha’s version of set-valued Ekeland’s variational principle
inferred← citeshttps://doi.org/10.1007/s10255-007-0374-3openalex-snapshot
Henig Efficiency in Vector Optimization with Nearly Cone-subconvexlike Set-valued Functions
inferred← citeshttps://doi.org/10.1007/s10255-018-0727-0openalex-snapshot
Optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps characterized by contingent epiderivative
inferred← citeshttps://doi.org/10.1007/s10255-019-0836-4openalex-snapshot
Higher-order Optimality Conditions and Duality for Approximate Solutions in Non-convex Set-valued Optimization
inferred← citeshttps://doi.org/10.1007/s10479-025-06589-6openalex-snapshot
Bilevel programming problems: a view through set-valued optimization
inferred← citeshttps://doi.org/10.1007/s10898-007-9165-xopenalex-snapshot
Characterizing efficiency without linear structure: a unified approach
inferred← citeshttps://doi.org/10.1007/s10898-012-9846-yopenalex-snapshot
Characterizations of the nonemptiness and compactness for solution sets of convex set-valued optimization problems
inferred← citeshttps://doi.org/10.1007/s10957-004-6472-yopenalex-snapshot
Some Variants of the Ekeland Variational Principle for a Set-Valued Map
inferred← citeshttps://doi.org/10.1007/s10957-007-9237-6openalex-snapshot
Lagrangian Duality in Set-Valued Optimization
inferred← citeshttps://doi.org/10.1007/s10957-007-9291-0openalex-snapshot
Superefficiency in Vector Optimization with Nearly Subconvexlike Set-Valued Maps
inferred← citeshttps://doi.org/10.1007/s10957-011-9952-xopenalex-snapshot
On Optimization Problems with Set-Valued Objective Maps: Existence and Optimality
inferred← citeshttps://doi.org/10.1007/s10957-013-0431-4openalex-snapshot
Lagrange Duality in Set Optimization
inferred← citeshttps://doi.org/10.1007/s10957-014-0679-3openalex-snapshot
Variational Inequalities Characterizing Weak Minimality in Set Optimization
inferred← citeshttps://doi.org/10.1007/s10957-023-02307-zopenalex-snapshot
Conjugate Duality in Set Optimization via Nonlinear Scalarization
inferred← citeshttps://doi.org/10.1007/s10957-024-02384-8openalex-snapshot
Cone-Compactness of a Set and Applications to Set-Equilibrium Problems
inferred← citeshttps://doi.org/10.1007/s10957-025-02739-9openalex-snapshot
Cone Sequential Compactness of a Set and an Application to Set Optimization Problems
inferred← citeshttps://doi.org/10.1007/s11117-024-01089-6openalex-snapshot
An algorithm to solve polytopic set optimization problem based on a partial set order relation
inferred← citeshttps://doi.org/10.1007/s11590-016-1027-3openalex-snapshot
Nonlinear scalarization functions and polar cone in set optimization
inferred← citeshttps://doi.org/10.1007/s11590-019-01531-9openalex-snapshot
Second-order optimality conditions for set optimization using coradiant sets
inferred← citeshttps://doi.org/10.1007/s12215-014-0163-9openalex-snapshot
Sufficient optimality conditions and duality theorems for set-valued optimization problem under generalized cone convexity
inferred← citeshttps://doi.org/10.1007/s12215-016-0258-6openalex-snapshot
Set-valued minimax programming problems under generalized cone convexity
inferred← citeshttps://doi.org/10.1007/s12597-025-00922-0openalex-snapshot
Sufficiency and duality for set-valued optimization problems with $$\kappa$$-cone arcwise connectedness of higher-order
inferred← citeshttps://doi.org/10.1007/s40305-025-00610-2openalex-snapshot
Lagrangian Duality in Set Optimization Problems based on Improvement Sets
inferred← citeshttps://doi.org/10.1007/s40306-020-00370-6openalex-snapshot
Continuity of Solution Maps to Parametric Set Optimization Problems via Parametric Equilibrium Problems
inferred← citeshttps://doi.org/10.1007/s40324-019-00209-7openalex-snapshot
Optimality conditions for set-valued minimax fractional programming problems
inferred← citeshttps://doi.org/10.1007/s40324-022-00295-0openalex-snapshot
On constrained set-valued optimization problems with $$\rho $$-cone arcwise connectedness
inferred← citeshttps://doi.org/10.1007/s40324-025-00390-yopenalex-snapshot
Set-valued minimax programming problems under higher-order $$\sigma $$-arcwisely connectivity
inferred← citeshttps://doi.org/10.1016/0362-546x(92)90044-fopenalex-snapshot
A saddlepoint theorem for set-valued maps
inferred← citeshttps://doi.org/10.1016/j.amc.2010.04.008openalex-snapshot
On optimization problems with set-valued objective maps
inferred← citeshttps://doi.org/10.1016/j.cam.2007.02.011openalex-snapshot
Higher-order Mond–Weir duality for set-valued optimization
inferred← citeshttps://doi.org/10.1016/j.ejor.2019.01.003openalex-snapshot
Primal worst and dual best in robust vector optimization
inferred← citeshttps://doi.org/10.1016/j.jmaa.2004.10.001openalex-snapshot
Optimality conditions for Henig and globally proper efficient solutions with ordering cone has empty interior
inferred← citeshttps://doi.org/10.1016/j.jmaa.2006.01.033openalex-snapshot
Nonconvex scalarization in set optimization with set-valued maps
inferred← citeshttps://doi.org/10.1016/j.jmaa.2014.10.010openalex-snapshot
A Minty variational principle for set optimization
inferred← citeshttps://doi.org/10.1016/j.na.2011.09.028openalex-snapshot
Pointwise well-posedness in set optimization with cone proper sets
inferred← citeshttps://doi.org/10.1016/j.omega.2004.07.004openalex-snapshot
Proximal proper efficiency in set-valued optimization
inferred← citeshttps://doi.org/10.1016/s0022-247x(02)00410-9openalex-snapshot
Nonconvex vector optimization of set-valued mappings
inferred← citeshttps://doi.org/10.1016/s0022-247x(02)00452-3openalex-snapshot
Super efficiency in vector optimization with nearly convexlike set-valued maps
inferred← citeshttps://doi.org/10.1016/s0022-247x(03)00192-6openalex-snapshot
Subdifferentials of multifunctions and Lagrange multipliers for multiobjective optimization
inferred← citeshttps://doi.org/10.1016/s0362-546x(01)00274-7openalex-snapshot
On set-valued optimization
inferred← citeshttps://doi.org/10.1016/s0362-546x(97)00213-7openalex-snapshot
On cone convexity of set-valued maps
inferred← citeshttps://doi.org/10.1017/s0004972700039290openalex-snapshot
The Strictly Efficient Subgradient of Set-Valued Optimisation
inferred← citeshttps://doi.org/10.1023/a:1004657412928openalex-snapshot
∈-Weak Minimal Solutions of Vector Optimization Problems with Set-Valued Maps
inferred← citeshttps://doi.org/10.1023/a:1008653120360openalex-snapshot
Optimization and Stability Results Through Cone Lower Semicontinuity
inferred← citeshttps://doi.org/10.1023/a:1015366419163openalex-snapshot
Characterizations of Solutions for Vector Equilibrium Problems
inferred← citeshttps://doi.org/10.1023/a:1017535631418openalex-snapshot
Near-Subconvexlikeness in Vector Optimization with Set-Valued Functions
inferred← citeshttps://doi.org/10.1023/a:1017581009670openalex-snapshot
Existence of a Solution and Variational Principles for Vector Equilibrium Problems
inferred← citeshttps://doi.org/10.1023/a:1019620812169openalex-snapshot
Existence of Efficient Points in Vector Optimization and Generalized Bishop–Phelps Theorem
inferred← citeshttps://doi.org/10.1023/a:1022658019642openalex-snapshot
Lagrangian Duality for Minimization of Nonconvex Multifunctions
inferred← citeshttps://doi.org/10.1023/a:1022676013609openalex-snapshot
Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps
inferred← citeshttps://doi.org/10.1023/a:1026407517917openalex-snapshot
Theorems of the Alternative and Optimization with Set-Valued Maps
inferred← citeshttps://doi.org/10.1051/ro/2016068openalex-snapshot
Approximate Lagrangian duality and saddle point optimality in set optimization
inferred← citeshttps://doi.org/10.1080/01630569208816480openalex-snapshot
Axiomatic approach to duality in optimization
inferred← citeshttps://doi.org/10.1080/01630569808816819openalex-snapshot
Set-valued derivatives of multifunctions and optimality conditions
inferred← citeshttps://doi.org/10.1080/02331930500096197openalex-snapshot
Optimization with set relations: conjugate duality
inferred← citeshttps://doi.org/10.1080/02331930802355374openalex-snapshot
ε-Conjugate maps andε-conjugate duality in vector optimization with set-valued maps
inferred← citeshttps://doi.org/10.1080/02331934.2013.766187openalex-snapshot
Lagrange duality, stability and subdifferentials in vector optimization
inferred← citeshttps://doi.org/10.1080/02331934.2016.1189550openalex-snapshot
Weak minimizers, minimizers and variational inequalities for set-valued functions. A blooming wreath?
inferred← citeshttps://doi.org/10.1080/02331934.2016.1271419openalex-snapshot
Approximate solutions and scalarization in set-valued optimization
inferred← citeshttps://doi.org/10.1080/02331934.2018.1556663openalex-snapshot
External and internal stability in set optimization
inferred← citeshttps://doi.org/10.1080/02331939308843868openalex-snapshot
Recession maps and applications
inferred← citeshttps://doi.org/10.1080/02331939608844241openalex-snapshot
Lagrange multipliers saddle points and scalarizations in composite multiobjective nonsmooth programming
inferred← citeshttps://doi.org/10.1080/02331939708844284openalex-snapshot
Optimality and duality for multiobjective programming involving subdifferentiable set functions
inferred← citeshttps://doi.org/10.1080/02331939708844289openalex-snapshot
A survey of recent[1985-1995]advances in generalized convexity with applications to duality theory and optimality conditions
inferred← citeshttps://doi.org/10.1080/02331939808844416openalex-snapshot
Necessary conditions for extremality and separation theorems with applications to multiobjective optimization
inferred← citeshttps://doi.org/10.1080/02522667.2003.10699556openalex-snapshot
Existence theorems of set optimization with set-valued maps
inferred← citeshttps://doi.org/10.1080/10556788.2025.2459841openalex-snapshot
Cone-compactness of a set and related topological properties: stability issues and applications
inferred← citeshttps://doi.org/10.1109/cso.2010.82openalex-snapshot
Convexity and Optimization of Set-Valued Mapping in Vector Space
inferred← citeshttps://doi.org/10.1109/tgrs.2020.3017937openalex-snapshot
X-SVM: An Extension of C-SVM Algorithm for Classification of High-Resolution Satellite Imagery
inferred← citeshttps://doi.org/10.1137/s1052623496311697openalex-snapshot
The Lagrange Multiplier Rule in Set-Valued Optimization
inferred← citeshttps://doi.org/10.1142/9789812792907_0005openalex-snapshot
VECTOR-VALUED MINIMAX THEOREMS IN MULTICRITERIA GAMES
inferred← citeshttps://doi.org/10.1155/2009/462637openalex-snapshot
Higher-Order Weakly Generalized Adjacent Epiderivatives and Applications to Duality of Set-Valued Optimization
inferred← citeshttps://doi.org/10.1155/2011/817965openalex-snapshot
Erratum for "Higher-Order Weakly Generalized Adjacent Epiderivatives and Applications to Duality of Set-Valued Optimization"
inferred← citeshttps://doi.org/10.1155/2011/839679openalex-snapshot
Tightly Proper Efficiency in Vector Optimization with Nearly Cone-Subconvexlike Set-Valued Maps
inferred← citeshttps://doi.org/10.1155/2013/105617openalex-snapshot
The Relationship between Two Kinds of Generalized Convex Set-Valued Maps in Real Ordered Linear Spaces
inferred← citeshttps://doi.org/10.1155/2013/570918openalex-snapshot
Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps
inferred← citeshttps://doi.org/10.1155/2013/573408openalex-snapshot
Lagrangian Duality for Multiobjective Programming Problems in Lexicographic Order
inferred← citeshttps://doi.org/10.11650/tjm.17.2013.1935openalex-snapshot
LAGRANGIAN DUALITY FOR VECTOR OPTIMIZATION PROBLEM WITH SET-VALUED MAPPINGS
inferred← citeshttps://doi.org/10.11650/twjm/1500405134openalex-snapshot
OPTIMIZATION THEORY FOR SET FUNCTIONS IN NONDIFFERENTIABLE FRACTIONAL PROGRAMMING WITH MIXED TYPE DUALITY
inferred← citeshttps://doi.org/10.11650/twjm/1500406282openalex-snapshot
Higher-order Generalized Adjacent Derivative and Applications to Duality for Set-valued Optimization
inferred← citeshttps://doi.org/10.1186/1029-242x-2014-406openalex-snapshot
Second-order composed contingent epiderivatives and set-valued vector equilibrium problems
inferred← citeshttps://doi.org/10.1287/moor.2020.1060openalex-snapshot
Set Relations via Families of Scalar Functions and Approximate Solutions in Set Optimization
inferred← citeshttps://doi.org/10.1360/n012019-00042openalex-snapshot
The linear scalarizations and Lagrange multipliers for vector optimization
inferred← citeshttps://doi.org/10.1515/jaa-2020-2042openalex-snapshot
Lagrangian multipliers for generalized affine and generalized convex vector optimization problems of set-valued maps
inferred← citeshttps://doi.org/10.1515/math-2018-0095openalex-snapshot
Optimality and duality in set-valued optimization utilizing limit sets
inferred← citeshttps://doi.org/10.19139/soic.v4i2.175openalex-snapshot
Optimality and duality in set-valued optimization using higher-order radial derivatives
inferred← citeshttps://doi.org/10.21203/rs.3.rs-3319677/v1openalex-snapshot
Set-valued minimax programming problems under higher-order σ-arcwisely connectivity
inferred← citeshttps://doi.org/10.22436/jnsa.005.05.06openalex-snapshot
On fuzzy order relations
inferred← citeshttps://doi.org/10.2298/fil1911457yopenalex-snapshot
Scalarization and well-posedness for set optimization using coradiant sets
inferred← citeshttps://doi.org/10.2298/yjor231215046dopenalex-snapshot
Higher-order Mond-Weir duality of set-valued fractional minimax programming problems
inferred← citeshttps://doi.org/10.2478/candc-2022-0004openalex-snapshot
Set-valued minimax fractional programming problems under ρ -cone arcwise connectedness
inferred← citeshttps://doi.org/10.28924/2291-8639-21-2023-63openalex-snapshot
Optimality Conditions for Set-Valued Optimization Problems
inferred← citeshttps://doi.org/10.3390/axioms10040302openalex-snapshot
On Constrained Set-Valued Semi-Infinite Programming Problems with ρ-Cone Arcwise Connectedness
inferred← citeshttps://doi.org/10.3390/math10060938openalex-snapshot
Mond-Weir and Wolfe Duality of Set-Valued Fractional Minimax Problems in Terms of Contingent Epi-Derivative of Second-Order
inferred← citeshttps://doi.org/10.37398/jsr.2020.640243openalex-snapshot
Optimality Conditions for Set-Valued Minimax Programming Problems via Second-Order Contingent Epiderivative
inferred← citeshttps://doi.org/10.3934/math.2023569openalex-snapshot
Set-valued minimax programming problems under $ \sigma $-arcwisely connectivity
inferred← citeshttps://doi.org/10.3934/naco.2014.4.309openalex-snapshot
Topological properties of Henig globally efficient solutions of set-valued problems
inferred← citeshttps://doi.org/10.48550/arxiv.1706.03728openalex-snapshot
Lagrangian Multipliers for Presubconvexlike Optimization Problems of Set Valued Functions
inferred← citeshttps://doi.org/10.48550/arxiv.1812.03300openalex-snapshot
Set Relations and Approximate Solutions in Set Optimization
inferred← citeshttps://doi.org/10.68381/jca11011openalex-snapshot
Closing the Duality Gap in Linear Vector Optimization
inferred← citeshttps://doi.org/10.68381/jca14020openalex-snapshot
Weak and Proper Efficiency in Set-Valued Optimization on Real Linear Spaces
Editorial review for independent work. ICSAC — the Institute for Complexity Science and Advanced Computing — runs a structured editorial panel for researchers publishing outside journals, and publishes on CiteStamp rails. Submission is free and goes through ORCID: icsacinstitute.org/submit.