Sentence examples for the primal problem of from inspiring English sources

The primal problem of CQSCO is given by min f ( x ) = 1 2 〈 x, Q ( x ) 〉 + 〈 c, x 〉 s.t.

We present a duality theory that converts the primal problem of selecting concentrations of species to make a pathway feasible to its dual problem of selecting linear combinations of reactions that make the pathway infeasible.

It has been stated that the primal problem of (4) is difficult to solve with efficient approaches, especially in large-scale HetNet with both macrocells and a number of pico-/femtocells.

We consider the primal problem of CQSDO in the standard form min { 1 2 X Q ( X ) + C X : A i X = b i, i = 1, 2, …, m, X ⪰ 0 }, and its dual problem max { − 1 2 X Q ( X ) + b T y : ∑ i = 1 m y i A i − Q ( X ) + S = C, S ⪰ 0 }.

We first derive a dual problem of the primal problem to demonstrate that there is no duality gap between them.

The main result of the paper establishes a rigorous equivalence between infeasibility of the primal problem and existence of a solution of the dual problem.

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.

Nevertheless the condition that allows determination of p∗(h) as the Lagrangian maximizer p(h,λ∗) [cf. (16)] is not the convexity of the primal problem but the lack of duality gap.

We show theoretically that our algorithm converges to the optimal solution of the primal problem by using the knowledge of stochastic programming.

They show theoretically that the algorithm converges to the optimal solution of the primal problem by using the knowledge of stochastic programming.

Let P denote the optimum value of the primal problem (20) and D that of its dual in (24) and assume there exists a strictly feasible point (x0,p0) that satisfies the constraints in (20) with strict inequality.