Sentence examples for values of the primal from inspiring English sources

where and given in (5) and (24) are the optimal values of the primal and dual problems.

In particular, the optimal values of the primal variables, i.e., {x j }, are obtained from an optimal value of the dual variable, i.e., μ ∗.

The value -Θ∗, or any feasible approximation -Θ to it, is thus an upper bound to the optimum value of the primal problem U∗.

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.

Moreover, as the virtual uplink sum power {λ 1,i,j } is upper bounded by real downlink power P max, and according to the duality theory [26], the optimal value of the dual objective function is lower bounded by the maximum value of the primal maximization problem (4).

The reduced costs are nonnegative and ξ ̄ ( x i ; s ), a i equals to 0 if the corresponding ρ ̄ ( x i ; s ), a ι > 0. It is also interpreted as the rate of decrease in the objective value of the primal linear program (16) per unit increase of variable ρ ( x i ; s ), a i.

The objective function value of the optimal solution (of primal or dual) is the efficiency score for unit o.

where the equality is true because P and p∗are the otpimal value and arguments of the primal optimization problem (2).

Let t l, x l, and p l denote the primal values of the l th user, and t l ′ and x l ′ denote the new values randomly chosen by the l th user.

Let r l and p l denote the primal values of the l th user, and r l ′ denote the new value randomly chosen by the l th user, which is treated as a new target transmission rate for the l th user.

The difference is called the duality gap of iteration, and it upper bounds the distance from the so far best found primal objective function value to the supremum of the primal objective function.