There is a corresponding duality in three-dimensional projective geometry between points and planes.
Conversely, given killing rates on the boundary, we construct the corresponding duality preserving extensions of the minimal processes that admit no jumps between the boundary points and have the prescribed killing rate at the boundary, by repeatedly doing one-point extension one at a time using Itô's Poisson point processes of excursions.
A mixed dual is proposed and corresponding duality results are obtained.
The corresponding duality gap is zero, that is, we have F boldsymbol{x}^)=D boldsymbol{lambda}^,boldsymbol{epsilon}^);.
Then, corresponding weak duality, strong duality, and converse duality theorems are established.
In Sections 4 and 5, we introduce a higher-order Mond-Weir type dual problem and a higher-order Wolfe type dual problem to a constrained set-valued optimization problem and establish corresponding weak duality, strong duality and converse duality theorems, respectively.
Further, the duality between corresponding parameters with dual indenters is explored.
The corresponding result to 'Sawyer duality principle' for this discrete case was proved in [10].
Motivated by various concepts of generalized convexity, Liang et al. [27] introduced a unified formulation of generalized convexity, called ( F, α, ρ, d ) -convexity and obtained corresponding optimality conditions and duality relations for a single objective fractional problem.
(3 If we replace -convexity by generalized -convexity, then our weak duality theorems reduce to the corresponding ones in Yang et al. [11].
Combining the dispersive estimate and a standard duality argument, we also derive the corresponding Strichartz inequalities.
