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The relationship between theorems of the alternative, least norm problems, steepest descent directions, and degeneracy: A review

https://doi.org/10.1007/bf02096256
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What this work says

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

inferredcites →https://doi.org/10.1002/0471787779.ch10openalex-snapshot
Methods of Feasible Directions
inferredcites →https://doi.org/10.1002/9781118723203openalex-snapshot
Practical Methods of Optimization
inferredcites →https://doi.org/10.1002/nav.3800270408openalex-snapshot
Solving multifacility location problems involving euclidean distances
inferredcites →https://doi.org/10.1002/nav.3800290116openalex-snapshot
A note on solving multifacility location problems involving euclidean distances
inferredcites →https://doi.org/10.1007/978-3-642-46216-0openalex-snapshot
Convexity and Optimization in Finite Dimensions I
inferredcites →https://doi.org/10.1007/978-94-011-7517-3_7openalex-snapshot
Non-linear Programming
inferredcites →https://doi.org/10.1007/bf00935321openalex-snapshot
Theorems of the alternative and optimality conditions
inferredcites →https://doi.org/10.1007/bf00935442openalex-snapshot
Theorems of the alternative and optimality conditions
inferredcites →https://doi.org/10.1007/bf00939458openalex-snapshot
The smallest point of a polytope
inferredcites →https://doi.org/10.1007/bf01442864openalex-snapshot
Ueber die Auflösung linearer Gleichungen mit reellen Coefficienten
inferredcites →https://doi.org/10.1007/bf01458147openalex-snapshot
�ber positive L�sungen homogener linearer Gleichungen
inferredcites →https://doi.org/10.1007/bf01580381openalex-snapshot
Finding the nearest point in A polytope
inferredcites →https://doi.org/10.1007/bf01580864openalex-snapshot
A new theorem of the alternative
inferredcites →https://doi.org/10.1007/bf02591853openalex-snapshot
A projected newton method forl p norm location problems
inferredcites →https://doi.org/10.1007/bf02591963openalex-snapshot
A quadratically convergent method for minimizing a sum of euclidean norms
inferredcites →https://doi.org/10.1007/bf02591990openalex-snapshot
A note on optimality conditions for the Euclidean. Multifacility location problem
inferredcites →https://doi.org/10.1007/bfb0093145openalex-snapshot
A second-order method for solving the continuous multifacility location problem
inferredcites →https://doi.org/10.1007/bfb0120703openalex-snapshot
A method of conjugate subgradients for minimizing nondifferentiable functions
inferredcites →https://doi.org/10.1007/bfb0121249openalex-snapshot
Algorithm for a least-distance programming problem
inferredcites →https://doi.org/10.1016/0024-3795(73)90047-5openalex-snapshot
A numerically stable form of the simplex algorithm
inferredcites →https://doi.org/10.1016/0024-3795(88)90067-5openalex-snapshot
Linear programming via least squares
inferredcites →https://doi.org/10.1016/s0022-0000(68)80034-0openalex-snapshot
Algorithms for some minimax problems
inferredcites →https://doi.org/10.1049/sqj.1970.0088openalex-snapshot
Optimization by Vector Space Methods
inferredcites →https://doi.org/10.1057/jors.1976.145openalex-snapshot
An Efficient Computational Procedure for Solving the Multi-Facility Rectilinear Facilities Location Problem
inferredcites →https://doi.org/10.1057/jors.1982.148openalex-snapshot
Practical Methods of Optimization. Vol. 2 -- Constrained Optimization
inferredcites →https://doi.org/10.1057/jors.1987.94openalex-snapshot
Theory of Linear and Integer Programming
inferredcites →https://doi.org/10.1080/00401706.1971.10488871openalex-snapshot
Integer and Nonlinear Programming
inferredcites →https://doi.org/10.1080/00401706.1987.10488303openalex-snapshot
Finite Algorithms in Optimization and Data Analysis
inferredcites →https://doi.org/10.1080/01630568708816231openalex-snapshot
An algorithm for non-negative norm minimal solutions
inferredcites →https://doi.org/10.1080/05695557008974767openalex-snapshot
Locating New Facilities with Respect to Existing Facilities
inferredcites →https://doi.org/10.1093/imanum/4.3.275openalex-snapshot
Discrete l 1 Approximation by Rational Functions
inferredcites →https://doi.org/10.1093/imanum/6.3.343openalex-snapshot
An Efficient Algorithm for Solving the Rectilinear Multifacility Location Problem
inferredcites →https://doi.org/10.1093/imanum/9.1.95openalex-snapshot
The Minimax Solution of Linear Equations Subject to Linear Constraints
inferredcites →https://doi.org/10.1137/0311049openalex-snapshot
A Descent Numerical Method for Optimization Problems with Nondifferentiable Cost Functionals
inferredcites →https://doi.org/10.1137/0312003openalex-snapshot
Finding the Point of a Polyhedron Closest to the Origin
inferredcites →https://doi.org/10.1137/0713027openalex-snapshot
A Descent Method for the Uniform Solution to Over-Determined Systems of Linear Equations
inferredcites →https://doi.org/10.1137/0715015openalex-snapshot
Minimization Techniques for Piecewise Differentiable Functions: The $l_1$ Solution to an Overdetermined Linear System
inferredcites →https://doi.org/10.1137/0715017openalex-snapshot
On Cline’s Direct Method for Solving Overdetermined Linear Systems in the $L_\infty $ Sense
inferredcites →https://doi.org/10.1137/0802029openalex-snapshot
On Regularized Least Norm Problems
inferredcites →https://doi.org/10.1137/0901037openalex-snapshot
A Stable Algorithm for Solving the Multifacility Location Problem Involving Euclidean Distances
inferredcites →https://doi.org/10.1137/0910021openalex-snapshot
The $l_1 $ Solution of Linear Equations Subject to Linear Constraints
inferredcites →https://doi.org/10.1137/1.9781611971255openalex-snapshot
Nonlinear Programming
inferredcites →https://doi.org/10.1137/1.9781611975604openalex-snapshot
Practical Optimization
inferredcites →https://doi.org/10.1145/103147.103155openalex-snapshot
On computational aspects of bounded linear least squares problems
inferredcites →https://doi.org/10.1145/355921.355930openalex-snapshot
Linearly Constrained Discrete I 1 Problems
inferredcites →https://doi.org/10.1515/9781400873173openalex-snapshot
Convex Analysis
inferredcites →https://doi.org/10.1515/crll.1902.124.1openalex-snapshot
Theorie der einfachen Ungleichungen.
inferredcites →https://doi.org/10.2307/1905734openalex-snapshot
A Note on Motzkin's Transposition Theorem
inferredcites →https://doi.org/10.2307/1910243openalex-snapshot
The Theory of Linear Economic Models
inferredcites →https://doi.org/10.2307/2343863openalex-snapshot
Nonlinear Programming.
inferredcites →https://doi.org/10.2307/253980openalex-snapshot
Theory of Linear and Integer Programming
inferredcites →https://doi.org/10.2307/3006664openalex-snapshot
The Theory of Linear Economic Models

What points at this work

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

inferred← citeshttps://doi.org/10.1007/978-1-4613-0241-4_10openalex-snapshot
New perspective on the theorems of alternative
inferred← citeshttps://doi.org/10.1007/bf02614441openalex-snapshot
Duality theorem for a generalized Fermat-Weber problem
inferred← citeshttps://doi.org/10.1016/j.csda.2004.07.007openalex-snapshot
The solution of linear inequalities
inferred← citeshttps://doi.org/10.1016/j.laa.2006.03.022openalex-snapshot
The distance between two convex sets
inferred← citeshttps://doi.org/10.1016/s1059-0560(99)00051-9openalex-snapshot
Looking for arbitrage
inferred← citeshttps://doi.org/10.1016/s1570-579x(01)80011-2openalex-snapshot
On Theory and Practice of Row Relaxation Methods
inferred← citeshttps://doi.org/10.1023/a:1014870904813openalex-snapshot
A Computational Approach to the Fundamental Theorem of Asset Pricing in a Single-Period Market
inferred← citeshttps://doi.org/10.1023/a:1015370617219openalex-snapshot
The Smallest Correction of an Inconsistent System of Linear Inequalities
inferred← citeshttps://doi.org/10.1023/a:1022644832111openalex-snapshot
Theorems of the Alternative and Duality
inferred← citeshttps://doi.org/10.1080/03081080600967820openalex-snapshot
Farkas' Lemma, other theorems of the alternative, and linear programming in infinite-dimensional spaces: a purely linear-algebraic approach
inferred← citeshttps://doi.org/10.1080/10556780108805831openalex-snapshot
On theorems of the alternative
inferred← citeshttps://doi.org/10.1080/10556789808805676openalex-snapshot
A simple algebraic proof of Farkas's lemma and related theorems
inferred← citeshttps://doi.org/10.1080/27684830.2022.2068740openalex-snapshot
Solving equations with real Jordan canonical forms
inferred← citeshttps://doi.org/10.1134/s008154381709005xopenalex-snapshot
A New Class of Theorems of the Alternative
inferred← citeshttps://doi.org/10.1134/s0965542518070072openalex-snapshot
A New Proof of the Kuhn–Tucker and Farkas Theorems
inferred← citeshttps://doi.org/10.1137/06067438openalex-snapshot
A Short Algebraic Proof of the Farkas Lemma
inferred← citeshttps://doi.org/10.1137/s0036144594295502openalex-snapshot
Classroom Note:An Elementary Proof of Farkas' Lemma
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