On A characterization of optimality in convex programming

1976 ◽  
Vol 11 (1) ◽  
pp. 81-88 ◽  
Author(s):  
A. Ben-Israel ◽  
A. Ben-Tal
Keyword(s):  
Convex Programming ◽  
Characterization Of Optimality

Characterization of the solution for the problems of strong and weak convex programming

2021 ◽  
Vol 212 (6) ◽  
Author(s):  
Sergey Ivanovitch Dudov ◽  
Mikhail Anatol'evich Osiptsev
Keyword(s):  
Convex Programming

A note on optimal inspection policy for stochastically deteriorating series systems

1991 ◽  
Vol 28 (4) ◽  
pp. 934-939 ◽  
Author(s):  
Yuping Qiu
Keyword(s):  
Necessary Conditions ◽  
Inspection Policy ◽  
Limiting Case ◽  
Series Systems ◽  
Special Case ◽  
Characterization Of Optimality

A counterexample is given to demonstrate that a previously proposed characterization of optimal inspection policy for series systems is not correct in the discounted case. A set of valid necessary conditions is provided which leads to the characterization of optimality for a special case. The limiting case of these necessary conditions is also examined.

scholarly journals Duality theorems for convex programming without constraint qualification

1984 ◽  
Vol 36 (2) ◽  
pp. 253-266 ◽  
Author(s):  
P. Kanniappan
Keyword(s):  
Convex Function ◽  
Convex Programming ◽  
Constraint Qualification ◽  
Constraint Qualifications ◽  
Convex Programming Problem ◽  
Duality Theorems ◽  
Finite Dimensional ◽  
Lower Semi ◽  
Continuous Convex Function

AbstractInvoking a recent characterization of Optimality for a convex programming problem with finite dimensional range without any constraint qualification given by Borwein and Wolkowicz, we establish duality theorems. These duality theorems subsume numerous earlier duality results with constraint qualifications. We apply our duality theorems in the case of the objective function being the sum of a positively homogeneous, lower-semi-continuous, convex function and a subdifferentiable convex function. We also study specific problems of the above type in this setting.

scholarly journals Facial reduction for a cone-convex programming problem

1981 ◽  
Vol 30 (3) ◽  
pp. 369-380 ◽  
Author(s):  
Jon M. Borwein ◽  
Henry Wolkowicz
Keyword(s):  
Dimensional Space ◽  
Convex Programming Problem ◽  
Finite Dimensional Space ◽  
Facial Reduction ◽  
Finite Dimensional ◽  
Arbitrary Convex ◽  
Lagrange Multiplier Theorem ◽  
Image Position ◽  
Characterization Of Optimality

AbstractIn this paper we study the abstract convex programwhere S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set and p and g are respectively convex and S (on Ω). We use the concept of a minimal cone for (P) to correct and strengthen a previous characterization of optimality for (P), see Theorem 3.2. The results presented here are used in a sequel to provide a Lagrange multiplier theorem for (P) which holds without any constraint qualification.

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