Geometry of optimality conditions and constraint qualifications: The convex case

1980 ◽  
Vol 19 (1) ◽  
pp. 32-60 ◽  
Author(s):  
Henry Wolkowicz
Keyword(s):  
Optimality Conditions ◽  
Constraint Qualifications ◽  
Convex Case

scholarly journals Optimality conditions for a cone-convex programming problem

1979 ◽  
Vol 27 (2) ◽  
pp. 141-162 ◽  
Author(s):  
Hélène M. Massam
Keyword(s):  
Vector Space ◽  
Optimality Conditions ◽  
Programming Problem ◽  
Convex Programming ◽  
Convex Cone ◽  
Constraint Qualifications ◽  
Closed Convex Cone ◽  
Convex Programming Problem ◽  
Nonnegative Orthant ◽  
Locally Convex

AbstractOptimality conditions without constraint qualifications are given for the convex programming problem: Maximize f(x) such that g(x) ∈ B, where f maps X into R and is concave, g maps X into Rm and is B-concave, X is a locally convex topological vector space and B is a closed convex cone containing no line. In the case when B is the nonnegative orthant, the results reduce to some of those obtained recently by Ben-Israel, Ben-Tal and Zlobec.

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