Sentence examples for as the primal problem from inspiring English sources

For strictly concave utility functions, the dual problem always gives the same solution as the primal problem.

As the primal problem is a convex optimization problem, there is no gap between the primal and dual problems.

That is, Algorithm 1 for the dual upper bound finds a solution as long as the primal problem is feasible.

The minimization of the energy of the primal problem as well as the minimization of the energy of the dual problem with respect to a design function lead to the primal and dual material residuals, respectively.

The primal problem can be formulated as follows by incorporating the discriminant function (3): (5) s.t.

We can formulate the primal problem (PP) as follows: (1).

First, we express the Lagrangian of the primal problem (5) as (6).

Note that the CSI uncertainty bounds ε=[ε 1,·,ε K ] T and λ are regarded as the given parameters for both the primal problem (P ε ) and its dual (D ε ).

Thanks to the linearity property of the expectation, the Lagrangian function of the primal problem (5) can be expressed as (6).

thus obtaining a solution to the primal problem (9) accordingly.

Hence, the primal problem in (5) is equivalent with the following optimization problem.