Sentence examples for a primal problem from inspiring English sources

Lurie thinks he has found a neat "solution" to a primal problem.

In a primal problem, both the objective function and all constraints are convex, this satisfies Slater's condition [32].

Given a primal problem (P), there are many ways to formulate the dual problem (DP) such that the weak and strong duality theorems hold true between the primal and dual pair of problems (P) and (DP).

The first problem is a primal optimization problem for determining the optimal enzyme manipulations, corresponding gene over-expression or repression, in metabolic networks without considering cell viability and metabolic adjustment.

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

(Rockafellar-Wets) 1. Zero duality gap Let (x ∗,z ∗ be a solution to the primal problem (14), and let be any maximizer of the dual function (17).

We remark that this problem is an approximation of the primal problem (15) where the set S is replaced by a convex combination of feasible points ( v ( 1 ), p ( 1 ) ), …, ( v ( L ), p ( L ) ) ⊂ S and where x ∈ R 2 and u k denote the Lagrangian multipliers associated with the constraints A T λ=w and α≥μ T(p Tx−p (k))+λ T v (k) of the master program, respectively.

We further develop a solution algorithm based on the Lagrangian decomposition for the primal problem and a space-time prism based method to reduce the solution search space.

Lemaréchal's problem was additively separable, and each summand function was non-convex; nonetheless, a solution to the dual problem provided a close approximation to the primal problem's optimal value.

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.

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