Sentence examples for dual models from inspiring English sources

The primal and dual models provide the quantities and prices, respectively.

Weak, strong and strict converse duality theorems are discussed for two types of the dual models.

Husain et al.[8] first formulated second-order dual models for a minimax fractional programming problem and established duality relations involving η-bonvex functions.

In Section 3, we derive weak and strong duality theorems relating to the nonsmooth MPEC and the two dual models under convexity and generalized convexity assumptions.

Lai and Lee [11] obtained duality theorems for two parameter-free dual models of nondifferentiable minimax fractional problem involving generalized convexity assumptions.

The notion of symmetric duality was developed significantly by Dantzig et al. [2], and the Wolfe dual models presented in [2].

Remark 4.1 If p = 0, then using (4.3), the above dual model becomes the dual model considered in [5, 11, 12].

Avanzi et al. [13] consider a periodic dividend strategy in the dual model.

As the dual model (11) is non-smooth and non-differentiable, the minimization is difficult.

I contrast these models with a dual model of adaptive explanation and design explanation.

Similar findings hold for the DUAL model and soil architectures other than macroporous.