Sentence examples for duality problem from inspiring English sources
In the standard C-SVM model, the optimization problem is transformed into a duality problem.
Investigating this duality problem, this paper also proposes DEA models for general network structures with two additional properties.
Then, by virtue of the epiderivative, we discuss a higher-order Mond-Weir type duality problem and a higher-order Wolfe type duality problem to a constrained set-valued optimization problem, respectively.
Under a network structure, however, two standard directions of modeling the production process may generally lead to a pair of multiplier and envelopment DEA models so that the outcomes are not necessarily equivalent, i.e. a network duality problem occurs.
Although, the duality problem has recently been addressed for specific cases of network structures, for more complex structures, DEA models have only been able to be developed by following either the envelopment form or multiplier form.
We apply this representation and solve the duality problem for the p-approximation property (p-AP), that is, if the dual space X∗ has the p-AP, then so does X.
Then, using two duality problems, we derive a posteriori (L^{2}(0,T;L^{2}(Omega))) error estimates for the scalar functions in Section 3.
Using some proper duality problems, we derive a posteriori (L^{2}(0,T;L^{2}(Omega))) error estimates for the scalar functions.
By virtue of the tangent derivative of a set-valued map introduced in [4], Sach and Craven [5] discussed Wolfe type duality and Mond-Weir type duality problems for a set-valued optimization problem.
With vector G-invexity, he proved new duality results for nonlinear differentiable multiobjective programming problems, and a number of new vector duality problems such as G-Mond-Weir, G-Wolfe and G-mixed dual vector problems to the primal one were defined in [21].
Finally, we consider the strong duality of problem (1.1); that is, there is no duality gap between the problem and the dual problem and has at least an optimal solution.
