On the public citation graph

Theorems of the alternative and optimality conditions

https://doi.org/10.1007/bf00935442
0 signed · 152 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 See whether every reference in this work resolves to a known work and none has been retracted — and get a dated CiteStamped badge you can embed.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/10.1007/3-540-06583-0_41openalex-snapshot
Penalty methods and augmented Lagrangians in nonlinear programming
inferredcites →https://doi.org/10.1007/bf00935321openalex-snapshot
Theorems of the alternative and optimality conditions
inferredcites →https://doi.org/10.1007/bf01584248openalex-snapshot
An elementary survey of general duality theory in mathematical programming
inferredcites →https://doi.org/10.1007/bf01584647openalex-snapshot
Exact penalty functions in nonlinear programming
inferredcites →https://doi.org/10.1007/bf01585523openalex-snapshot
Fenchel and Lagrange duality are equivalent
inferredcites →https://doi.org/10.1016/0022-247x(71)90214-9openalex-snapshot
Asymptotic duality over closed convex sets
inferredcites →https://doi.org/10.1016/0022-247x(73)90240-0openalex-snapshot
A theorem of the alternative with application to convex programming: Optimality, duality, and stability
inferredcites →https://doi.org/10.1090/s0002-9939-1975-0395848-1openalex-snapshot
Duality Theorems and Theorems of the Alternative
inferredcites →https://doi.org/10.1137/0117120openalex-snapshot
Extensions of Lagrange Multipliers in Nonlinear Programming
inferredcites →https://doi.org/10.1137/0312021openalex-snapshot
Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming
inferredcites →https://doi.org/10.1137/1.9781611971255openalex-snapshot
Nonlinear Programming
inferredcites →https://doi.org/10.1287/opre.11.3.399openalex-snapshot
Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources
inferredcites →https://doi.org/10.1287/opre.19.4.1026openalex-snapshot
Nonlinear Pricing: Applications to Concave Programming

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/10.1007/0-306-48026-3_11openalex-snapshot
On the Existence of Solutions to Vector Optimization Problems
inferred← citeshttps://doi.org/10.1007/0-387-24276-7_54openalex-snapshot
Survey on the Fenchel Problem of Level Sets
inferred← citeshttps://doi.org/10.1007/0-387-25570-2_1openalex-snapshot
Unilateral Analysis and Duality
inferred← citeshttps://doi.org/10.1007/978-1-4613-0279-7_4openalex-snapshot
Some Remarks on Minimum Principles
inferred← citeshttps://doi.org/10.1007/978-1-4613-0299-5_11openalex-snapshot
On the Theory of Vector Optimization and Variational Inequalities. Image Space Analysis and Separation
inferred← citeshttps://doi.org/10.1007/978-1-4613-0299-5_22openalex-snapshot
On Vector Complementarity Systems and Vector Variational Inequalities
inferred← citeshttps://doi.org/10.1007/978-1-4757-2878-1_14openalex-snapshot
Separation and regularity in the image space
inferred← citeshttps://doi.org/10.1007/978-1-4757-2878-1_19openalex-snapshot
Variable metric methods along geodetics
inferred← citeshttps://doi.org/10.1007/978-1-4757-3226-9_11openalex-snapshot
Separation methods for Vector Variational Inequalities. Saddle point and gap function
inferred← citeshttps://doi.org/10.1007/978-1-4757-6019-4_12openalex-snapshot
Necessary Optimality Conditions via Image Problem
inferred← citeshttps://doi.org/10.1007/978-1-4899-0289-4_2openalex-snapshot
On Regularity for Generalized Systems and Applications
inferred← citeshttps://doi.org/10.1007/978-1-4899-1358-6_1openalex-snapshot
On a Separation Approach to Variational Inequalities
inferred← citeshttps://doi.org/10.1007/978-1-4899-1358-6_15openalex-snapshot
Variational and Quasi-Variational Inequalities in Network Flow Models. Recent Developments in Theory and Algorithms
inferred← citeshttps://doi.org/10.1007/978-1-4899-1358-6_18openalex-snapshot
Tensor Approximations of Smooth Nonlinear Complementarity Systems
inferred← citeshttps://doi.org/10.1007/978-1-4899-1358-6_3openalex-snapshot
On the Duality Theory for Finite Dimensional Variational Inequalities
inferred← citeshttps://doi.org/10.1007/978-1-4899-1358-6_9openalex-snapshot
Separation of Sets and Gap Functions for Quasi-Variational Inequalities
inferred← citeshttps://doi.org/10.1007/978-3-642-21114-0_6openalex-snapshot
Optimality Conditions and Image Space Analysis for Vector Optimization Problems
inferred← citeshttps://doi.org/10.1007/978-3-642-46709-7_17openalex-snapshot
An Approach to Lagrangian Duality in Vector Optimization
inferred← citeshttps://doi.org/10.1007/978-3-642-46802-5_13openalex-snapshot
Regularity conditions for constrained extremum problems via image space approach: the linear case
inferred← citeshttps://doi.org/10.1007/978-3-642-46802-5_26openalex-snapshot
Generalized concavity and optimality conditions in vector and scalar optimization
inferred← citeshttps://doi.org/10.1007/978-3-642-57014-8_25openalex-snapshot
Recent Advances on Second-Order Optimality Conditions
inferred← citeshttps://doi.org/10.1007/978-94-009-0369-2_1openalex-snapshot
General Optimality Conditions via a Separation Scheme
inferred← citeshttps://doi.org/10.1007/bf00047497openalex-snapshot
Characterizing optimality in mathematical programming models
inferred← citeshttps://doi.org/10.1007/bf00938802openalex-snapshot
On the image of a constrained extremum problem and some applications to the existence of a minimum
inferred← citeshttps://doi.org/10.1007/bf00939083openalex-snapshot
Theorems of the alternative for multifunctions with applications to optimization: General results
inferred← citeshttps://doi.org/10.1007/bf00939578openalex-snapshot
Lagrange multipliers and generalized differentiable functions in vector extremum problems
inferred← citeshttps://doi.org/10.1007/bf00939933openalex-snapshot
On a Lagrangian sufficient optimality condition
inferred← citeshttps://doi.org/10.1007/bf00940005openalex-snapshot
Semidifferentiable functions and necessary optimality conditions
inferred← citeshttps://doi.org/10.1007/bf00940506openalex-snapshot
Tangent cones and Dini derivatives
inferred← citeshttps://doi.org/10.1007/bf00940645openalex-snapshot
An extension of the Hestenes necessary condition
inferred← citeshttps://doi.org/10.1007/bf00940768openalex-snapshot
On the reciprocal vector optimization problems
inferred← citeshttps://doi.org/10.1007/bf00940770openalex-snapshot
Regularity conditions for constrained extremum problems
inferred← citeshttps://doi.org/10.1007/bf00941576openalex-snapshot
New proof of a theorem of F. Giannessi
inferred← citeshttps://doi.org/10.1007/bf02032131openalex-snapshot
On some connections among variational inequalities, combinatorial and continuous optimization
inferred← citeshttps://doi.org/10.1007/bf02096256openalex-snapshot
The relationship between theorems of the alternative, least norm problems, steepest descent directions, and degeneracy: A review
inferred← citeshttps://doi.org/10.1007/bf02190319openalex-snapshot
Image of a parametric optimization problem and continuity of the perturbation function
inferred← citeshttps://doi.org/10.1007/bf02191781openalex-snapshot
Sufficient conditions for the existence of multipliers and Lagrangian duality in abstract optimization problems
inferred← citeshttps://doi.org/10.1007/bf02192090openalex-snapshot
Nonlinear coordinate representations of smooth optimization problems
inferred← citeshttps://doi.org/10.1007/bf02192647openalex-snapshot
Coercivity and image of constrained extremum problems
inferred← citeshttps://doi.org/10.1007/bf02196591openalex-snapshot
Regularity conditions for constrained extremum problems via image space
inferred← citeshttps://doi.org/10.1007/bf02207777openalex-snapshot
On the connectedness of the solution set to linear complementarity systems
inferred← citeshttps://doi.org/10.1007/bfb0076702openalex-snapshot
Non-linear separation theorems, duality and optimality conditions
inferred← citeshttps://doi.org/10.1007/s10898-008-9301-2openalex-snapshot
Separation of sets and Wolfe duality
inferred← citeshttps://doi.org/10.1007/s10898-009-9445-8openalex-snapshot
Some applications of the image space analysis to the duality theory for constrained extremum problems
inferred← citeshttps://doi.org/10.1007/s10898-011-9674-5openalex-snapshot
On the image space analysis for vector quasi-equilibrium problems with a variable ordering relation
inferred← citeshttps://doi.org/10.1007/s10898-013-0073-yopenalex-snapshot
Vector quasi-equilibrium problems: separation, saddle points and error bounds for the solution set
inferred← citeshttps://doi.org/10.1007/s10898-013-0093-7openalex-snapshot
Nonlinear separation approach for the augmented Lagrangian in nonlinear semidefinite programming
inferred← citeshttps://doi.org/10.1007/s10957-005-6398-zopenalex-snapshot
Local Convexity on Smooth Manifolds
inferred← citeshttps://doi.org/10.1007/s10957-006-9140-6openalex-snapshot
Generalized Motzkin Theorems of the Alternative and Vector Optimization Problems
inferred← citeshttps://doi.org/10.1007/s10957-007-9221-1openalex-snapshot
Lagrangian Duality and Cone Convexlike Functions
inferred← citeshttps://doi.org/10.1007/s10957-008-9360-zopenalex-snapshot
Fenchel Problem of Level Sets
inferred← citeshttps://doi.org/10.1007/s10957-009-9519-2openalex-snapshot
Regularity Conditions in Differentiable Vector Optimization Revisited
inferred← citeshttps://doi.org/10.1007/s10957-009-9531-6openalex-snapshot
Image Space Analysis and Scalarization of Multivalued Optimization
inferred← citeshttps://doi.org/10.1007/s10957-009-9598-0openalex-snapshot
Separation Approach for Augmented Lagrangians in Constrained Nonconvex Optimization
inferred← citeshttps://doi.org/10.1007/s10957-010-9657-6openalex-snapshot
Image Space Analysis and Scalarization for ε-Optimization of Multifunctions
inferred← citeshttps://doi.org/10.1007/s10957-010-9691-4openalex-snapshot
Image Space Analysis for Vector Variational Inequalities with Matrix Inequality Constraints and Applications
inferred← citeshttps://doi.org/10.1007/s10957-010-9710-5openalex-snapshot
Structure and Weak Sharp Minimum of the Pareto Solution Set for Piecewise Linear Multiobjective Optimization
inferred← citeshttps://doi.org/10.1007/s10957-012-0027-4openalex-snapshot
Nonlinear Separation Approach to Constrained Extremum Problems
inferred← citeshttps://doi.org/10.1007/s10957-012-0242-zopenalex-snapshot
Optimality Conditions for Generalized Ky Fan Quasi-Inequalities with Applications
inferred← citeshttps://doi.org/10.1007/s10957-013-0276-xopenalex-snapshot
A Unified Approach for Constrained Extremum Problems: Image Space Analysis
inferred← citeshttps://doi.org/10.1007/s10957-013-0358-9openalex-snapshot
Some Results on Augmented Lagrangians in Constrained Global Optimization via Image Space Analysis
inferred← citeshttps://doi.org/10.1007/s10957-013-0467-5openalex-snapshot
Unified Duality Theory for Constrained Extremum Problems. Part II: Special Duality Schemes
inferred← citeshttps://doi.org/10.1007/s10957-013-0468-4openalex-snapshot
Unified Duality Theory for Constrained Extremum Problems. Part I: Image Space Analysis
inferred← citeshttps://doi.org/10.1007/s10957-014-0634-3openalex-snapshot
On Saddle Points in Semidefinite Optimization via Separation Scheme
inferred← citeshttps://doi.org/10.1007/s10957-014-0686-4openalex-snapshot
Stability and Scalarization in Vector Optimization Using Improvement Sets
inferred← citeshttps://doi.org/10.1007/s10957-015-0736-6openalex-snapshot
Vector Variational-Like Inequalities with Constraints: Separation and Alternative
inferred← citeshttps://doi.org/10.1007/s10957-016-0880-7openalex-snapshot
Image Convexity of Generalized Systems with Infinite-Dimensional Image and Applications
inferred← citeshttps://doi.org/10.1007/s10957-016-1027-6openalex-snapshot
Image Space Analysis to Lagrange-Type Duality for Constrained Vector Optimization Problems with Applications
inferred← citeshttps://doi.org/10.1007/s10957-016-1029-4openalex-snapshot
Separation Functions and Optimality Conditions in Vector Optimization
inferred← citeshttps://doi.org/10.1007/s10957-016-1041-8openalex-snapshot
Set-Valued Systems with Infinite-Dimensional Image and Applications
inferred← citeshttps://doi.org/10.1007/s10957-017-1182-4openalex-snapshot
Refinements on Gap Functions and Optimality Conditions for Vector Quasi-Equilibrium Problems via Image Space Analysis
inferred← citeshttps://doi.org/10.1007/s10957-017-1197-xopenalex-snapshot
Image Space Analysis for Constrained Inverse Vector Variational Inequalities via Multiobjective Optimization
inferred← citeshttps://doi.org/10.1007/s10957-018-1216-6openalex-snapshot
Constrained Extremum Problems, Regularity Conditions and Image Space Analysis. Part I: The Scalar Finite-Dimensional Case
inferred← citeshttps://doi.org/10.1007/s10957-018-1247-zopenalex-snapshot
Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions
inferred← citeshttps://doi.org/10.1007/s10957-018-1325-2openalex-snapshot
Separations and Optimality of Constrained Multiobjective Optimization via Improvement Sets
inferred← citeshttps://doi.org/10.1007/s10957-019-01486-yopenalex-snapshot
Proper or Weak Efficiency via Saddle Point Conditions in Cone-Constrained Nonconvex Vector Optimization Problems
inferred← citeshttps://doi.org/10.1007/s10957-019-01505-yopenalex-snapshot
Characterizations of Multiobjective Robustness via Oriented Distance Function and Image Space Analysis
inferred← citeshttps://doi.org/10.1007/s10957-019-01543-6openalex-snapshot
Nonlinear Separation Approach to Inverse Variational Inequalities in Real Linear Spaces
inferred← citeshttps://doi.org/10.1007/s10957-021-01939-3openalex-snapshot
Image Space Analysis for Set Optimization Problems with Applications
inferred← citeshttps://doi.org/10.1007/s11117-012-0160-1openalex-snapshot
On maximum and variational principles via image space analysis
inferred← citeshttps://doi.org/10.1007/s11117-015-0343-7openalex-snapshot
A new approach to constrained optimization via image space analysis
inferred← citeshttps://doi.org/10.1007/s11117-016-0450-0openalex-snapshot
Nonlinear separation in the image space with applications to constrained optimization
inferred← citeshttps://doi.org/10.1007/s11425-011-4287-5openalex-snapshot
Image space analysis for variational inequalities with cone constraints and applications to traffic equilibria
inferred← citeshttps://doi.org/10.1007/s11590-011-0316-0openalex-snapshot
On Lagrangian duality in vector optimization: applications to the linear case
inferred← citeshttps://doi.org/10.1007/s11590-013-0644-3openalex-snapshot
Nonlinear separation functions and constrained extremum problems
inferred← citeshttps://doi.org/10.1007/s11590-015-0879-2openalex-snapshot
Nonlinear separation functions, optimality conditions and error bounds for Ky Fan quasi-inequalities
inferred← citeshttps://doi.org/10.1007/s11590-017-1109-xopenalex-snapshot
Nonlinear separation concerning E-optimal solution of constrained multi-objective optimization problems
inferred← citeshttps://doi.org/10.1007/s11590-017-1118-9openalex-snapshot
Saddle points and gap functions for weak generalized Ky Fan inequalities
inferred← citeshttps://doi.org/10.1007/s11590-018-1365-4openalex-snapshot
Conjugate duality for constrained optimization via image space analysis and abstract convexity
inferred← citeshttps://doi.org/10.1007/s11750-026-00716-7openalex-snapshot
A note on constraint qualification for saddle point conditions involving convex and linear affine functions
inferred← citeshttps://doi.org/10.1007/s40096-018-0256-2openalex-snapshot
Vector optimization using improvement sets in locally convex spaces
inferred← citeshttps://doi.org/10.1007/s40819-015-0123-xopenalex-snapshot
Quadratic Interpolation Technique to Minimize Univariable Fuzzy Functions
inferred← citeshttps://doi.org/10.1016/0022-247x(91)90221-kopenalex-snapshot
Inequality systems and optimization
inferred← citeshttps://doi.org/10.1016/0022-247x(92)90123-uopenalex-snapshot
On nonlinear programming in complex spaces
inferred← citeshttps://doi.org/10.1016/0377-2217(85)90313-3openalex-snapshot
On a pair of nonlinear mixed integer programming problems
inferred← citeshttps://doi.org/10.1016/j.mcm.2011.01.034openalex-snapshot
A new characterization of (weak) Pareto optimality for differentiable vector optimization problems with G -invex functions
inferred← citeshttps://doi.org/10.1023/a:1004641726264openalex-snapshot
On Convex Generalized Systems
inferred← citeshttps://doi.org/10.1023/a:1011938519299openalex-snapshot
Extended Lagrange and Penalty Functions in Optimization
inferred← citeshttps://doi.org/10.1023/a:1017566406216openalex-snapshot
On Global Optimality Conditions via Separation Functions
inferred← citeshttps://doi.org/10.1023/a:1021738714110openalex-snapshot
Regularity Conditions for the Linear Separation of Sets
inferred← citeshttps://doi.org/10.1023/a:1021781308794openalex-snapshot
Theorems of the Alternative and Optimality Conditions for Convexlike and General Convexlike Programming
inferred← citeshttps://doi.org/10.1023/a:1021890328184openalex-snapshot
Regularity Conditions in Vector Optimization
inferred← citeshttps://doi.org/10.1023/a:1022698811948openalex-snapshot
Separation of Sets, Lagrange Multipliers, and Totally Regular Extremum Problems
inferred← citeshttps://doi.org/10.1023/a:1022927915135openalex-snapshot
Lagrange-Type Functions in Constrained Optimization
inferred← citeshttps://doi.org/10.1023/b:jogo.0000015309.88480.2bopenalex-snapshot
On augmented Lagrangians for Optimization Problems with a Single Constraint
inferred← citeshttps://doi.org/10.1023/b:jogo.0000026452.32070.99openalex-snapshot
On necessary conditions for infinite-dimensional extremum problems
inferred← citeshttps://doi.org/10.1023/b:jota.0000037687.36868.5aopenalex-snapshot
On the Image Regularity Condition
inferred← citeshttps://doi.org/10.1051/cocv/2018012openalex-snapshot
Strong Lagrange duality and the maximum principle for nonlinear discrete time optimal control problems
inferred← citeshttps://doi.org/10.1080/00036811.2011.614603openalex-snapshot
Nonlinear separation in the image space with applications to penalty methods
inferred← citeshttps://doi.org/10.1080/00036811.2017.1325471openalex-snapshot
Characterization of duality for a generalized quasi-equilibrium problem
inferred← citeshttps://doi.org/10.1080/00036811.2018.1506105openalex-snapshot
Optimality conditions for vector optimization problems with non-cone constraints in image space
inferred← citeshttps://doi.org/10.1080/02331930500138536openalex-snapshot
Multipliers and general Lagrangians
inferred← citeshttps://doi.org/10.1080/02331931003610781openalex-snapshot
Conic separation for vector optimization problems
inferred← citeshttps://doi.org/10.1080/02331934.2010.505651openalex-snapshot
Image space approach and subdifferentials of integral functionals
inferred← citeshttps://doi.org/10.1080/02331934.2014.972954openalex-snapshot
Image space analysis and separation forG-semidifferentiable vector problems
inferred← citeshttps://doi.org/10.1080/02331934.2015.1014479openalex-snapshot
A new nonlinear scalarization function and applications
inferred← citeshttps://doi.org/10.1080/02331934.2016.1149584openalex-snapshot
Nonlinear separation approach to inverse variational inequalities
inferred← citeshttps://doi.org/10.1080/02331934.2019.1625352openalex-snapshot
Characterizations of multiobjective robustness on vectorization counterparts
inferred← citeshttps://doi.org/10.1080/02331938508843061openalex-snapshot
Convexlike alternative theorems and mathematical programming
inferred← citeshttps://doi.org/10.1080/02331938708843207openalex-snapshot
Generalized connectedness for families of Arcs
inferred← citeshttps://doi.org/10.1080/02331938708843228openalex-snapshot
Nonconvex theorems of the alternative and minimization
inferred← citeshttps://doi.org/10.1080/02331938908843428openalex-snapshot
Theorems of the alternative for set-valued functions in infinite-dimensional spaces
inferred← citeshttps://doi.org/10.1080/02331938908843499openalex-snapshot
Some results on regularity in vector optimization
inferred← citeshttps://doi.org/10.1080/02522667.1996.10699288openalex-snapshot
On nonlinear scalarization in vector optimization
inferred← citeshttps://doi.org/10.1137/13094606xopenalex-snapshot
Characterizing FJ and KKT Conditions in Nonconvex Mathematical Programming with Applications
inferred← citeshttps://doi.org/10.1142/9789812798862_0007openalex-snapshot
IMAGES, SEPARATION OF SETS AND EXTREMUM PROBLEMS
inferred← citeshttps://doi.org/10.1155/2012/370654openalex-snapshot
A Generalized Alternative Theorem of Partial and Generalized Cone Subconvexlike Set‐Valued Maps and Its Applications in Linear Spaces
inferred← citeshttps://doi.org/10.1155/2013/129319openalex-snapshot
Numerical and Analytical Methods for Variational Inequalities and Related Problems 2013
inferred← citeshttps://doi.org/10.1155/2013/245485openalex-snapshot
Variational Inequalities and Vector Optimization
inferred← citeshttps://doi.org/10.1155/2013/439394openalex-snapshot
Vector and Ordered Variational Inequalities and Applications to Order-Optimization Problems on Banach Lattices
inferred← citeshttps://doi.org/10.11650/twjm/1500405393openalex-snapshot
A SEPARATION APPROACH TO VECTOR QUASI-EQUILIBRIUM PROBLEMS: SADDLE POINT AND GAP FUNCTION
inferred← citeshttps://doi.org/10.1287/moor.11.1.30openalex-snapshot
On the Duality Gap in Nonconvex Optimization
inferred← citeshttps://doi.org/10.1287/opre.1110.1014openalex-snapshot
Piecewise Linear Multicriteria Programs: The Continuous Case and Its Discontinuous Generalization
inferred← citeshttps://doi.org/10.17265/2328-2142/2017.03.002openalex-snapshot
On a Multi-criterion Problem of Planning Maritime Cargo Transportation
inferred← citeshttps://doi.org/10.23952/jnva.4.2020.1.02openalex-snapshot
Some topics in vector optimization via image space analysis
inferred← citeshttps://doi.org/10.2991/icemct-15.2015.252openalex-snapshot
Necessary Optimality Condition for Vector Optimization Problems in Infinite-dimensional Linear Spaces
inferred← citeshttps://doi.org/10.3934/jimo.2016.12.1187openalex-snapshot
Semidefinite programming via image space analysis
inferred← citeshttps://doi.org/10.68381/jca04005openalex-snapshot
A Systematization of Convexity Concepts for Sets and Functions
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.