A simple proof of a general duality theorem of convex programming

1969 ◽  
Vol 13 (1) ◽  
pp. 29-36 ◽  
Author(s):  
B. Hohenbalken
Keyword(s):  
Convex Programming ◽  
Simple Proof ◽  
Duality Theorem ◽  
General Duality

scholarly journals On converse duality for a nondifferentiable program

1982 ◽  
Vol 25 (1) ◽  
pp. 71-80 ◽  
Author(s):  
T.R. Gulati
Keyword(s):  
Simple Proof ◽  
Duality Theorem ◽  
Constraint Qualification ◽  
Dual Problem ◽  
Linear Constraints ◽  
Simple Condition ◽  
Converse Duality ◽  
Slater Constraint Qualification ◽  
Converse Duality Theorem ◽  
Fritz John Conditions

A nonlinear nondifferentiable program with linear constraints is considered and a converse duality theorem is discussed. First we weaken an assumption previously made by Bhatia, and then give a simple proof under this weaker hypothesis, using the Fritz John conditions. Finally, defining a generalized Slater constraint qualification which implies Abadie's constraint qualification, we give a simple condition for the dual problem to satisfy this constraint qualification.

scholarly journals A general duality theorem for the Monge–Kantorovich transport problem

2012 ◽  
Vol 209 (2) ◽  
pp. 151-167 ◽  
Author(s):  
Mathias Beiglböck ◽  
Christian Léonard ◽  
Walter Schachermayer
Keyword(s):  
Duality Theorem ◽  
Transport Problem ◽  
General Duality

scholarly journals Duality theorems and an optimality condition for non-differentiable convex programming

1982 ◽  
Vol 32 (3) ◽  
pp. 369-379 ◽  
Author(s):  
P. Kanniappan ◽  
Sundaram M. A. Sastry
Keyword(s):  
Convex Function ◽  
Objective Function ◽  
Programming Problem ◽  
Convex Programming ◽  
Duality Theorem ◽  
Sufficient Optimality Conditions ◽  
Convex Programming Problem ◽  
Lower Semi ◽  
Continuous Convex Function ◽  
Necessary And Sufficient

AbstractNecessary and sufficient optimality conditions of Kuhn-Tucker type for a convex programming problem with subdifferentiable operator constraints have been obtained. A duality theorem of Wolfe's type has been derived. Assuming that the objective function is strictly convex, a converse duality theorem is obtained. The results are then applied to a programming problem in which the objective function is the sum of a positively homogeneous, lower-semi-continuous, convex function and a continuous convex function.

A general duality theorem for marginal problems

1995 ◽  
Vol 101 (3) ◽  
pp. 311-319 ◽  
Author(s):  
D. Ramachandran ◽  
L. R�schendorf
Keyword(s):  
Duality Theorem ◽  
General Duality

scholarly journals On duality in complex linear programming

1973 ◽  
Vol 16 (2) ◽  
pp. 172-175 ◽  
Author(s):  
B. D. Craven ◽  
B. Mond
Keyword(s):  
Linear Programming ◽  
Simple Proof ◽  
Duality Theorem ◽  
Complex Space ◽  
Real Space ◽  
Complex Case ◽  
Linear Programs ◽  
Polyhedral Convex ◽  
Complex Linear ◽  
Real Linear

In [3], Levinson proved a duality theorem for linear programming in complex space. Ben-Israel [1] generalized this result to polyhedral convex cones in complex space. In this paper, we give a simple proof of Ben-Israel's result based directly on the duality theorem for linear programming in real space. The explicit relations shown between complex and real linear programs should be useful in actually computing a solution for the complex case. We also give a simple proof of Farkas' theorem, generalized to polyhedral cones in complex space ([1], Theorem 3.5); the proof depends only on the classical form of Farkas' theorem for real space.

The theory of truth tabular connectives, both truth functional and modal

1997 ◽  
Vol 31 (4) ◽  
pp. 593-608 ◽  
Author(s):  
Gerald J. Massey
Keyword(s):  
Modal Logic ◽  
Duality Theorem ◽  
Functional Completeness ◽  
Partial Truth ◽  
Intuitive Concept ◽  
Close Investigation ◽  
General Duality ◽  
Truth Tables

Briefly, the following things are done in this paper. An informal exposition of the significance of partial truth tables in modal logic is presented. The intuitive concept of a truth tabular sentence connective is examined and made precise. From among a vast assortment of truth tabular connectives, the semantically well-behaved ones (called regular connectives) are singled out for close investigation. The familiar concept of functional completeness is generalized to all sets of regular connectives, and the functional completeness (or incompleteness) of selected sets of connectives is established. Some modal analogues of Sheffer's stroke are presented, i.e., single connectives are introduced which serve to define not only the truth functional connectives but all the regular modal connectives as well. The notion of duality is extended to all regular connectives and a general duality theorem is proved. Lastly, simplified proofs are given of several metatheorems about the system S5.

Mixed H2/H∞ control via convex programming

1991 ◽  
Author(s):  
Mario A. Rotea ◽  
Pramod P. Khargonekar
Keyword(s):  
Convex Programming
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