converse duality theorem
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Author(s):  
V. Jeyakumar

AbstractA duality theorem of Wolfe for nonlinear differentiable programs is extended to nondifferentiable programs with strong and weak convex functions, by replacing gradients by local subgradient. A converse duality theorem is also proved.


1982 ◽  
Vol 25 (1) ◽  
pp. 71-80 ◽  
Author(s):  
T.R. Gulati

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.


1979 ◽  
Vol 20 (3) ◽  
pp. 397-406 ◽  
Author(s):  
B. Mond ◽  
B.D. Craven

A duality theorem, and a converse duality theorem, are proved for a nonlinear fractional program, where the numerator of the objective function involves a concave function, not necessarily differentiable, and also the support function of a convex set, and the denominator involves a convex function, and the support function of a convex set. Various known results are deduced as special cases.


Author(s):  
Bertram Mond ◽  
Murray Schechter

AbstractWe consider a programming problem in which the objective function is the sum of a differentiable function and the p norm of Sx, where S is a matrix and p > 1. The constraints are inequality constraints defined by differentiable functions. With the aid of a recent transposition theorem of Schechter we get a duality theorem and also a converse duality theorem for this problem. This result generalizes a result of Mond in which the objective function contains the square root of a positive semi-definite quadratic function.


1975 ◽  
Vol 13 (3) ◽  
pp. 421-427 ◽  
Author(s):  
J. Parida

In this note a converse duality theorem is proved for a class of nonlinear programming problems over polyhedral cones in finite dimensional complex space by a direct use of a Kuhn-Tucker type necessary and sufficient condition for constrained optimization in complex space.


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