Sentence examples for by solving the subproblem from inspiring English sources

A global power allocation solution can be obtained by solving the subproblem of all nodes iteratively.

Case 3: Besides these two cases, the solution of problem (26) is obtained by solving the subproblem (29).

For each point (varvec{lambda }[k]), each MG minimizes its contribution to the Lagrangian function by solving the local subproblem (27) and determining the minimum point.

At each iterative point (x_{k}) in our method, the trial step (d_{k}) is obtained by solving the following subproblem: min q_{k}(d)=frac{1}{2}Vert F_{k}+ gamma_{k}dVert ^{2} quadtext{such that} quad Vert d Vert leDelta_{k}, (5) where (gamma_{k}) is the spectral coefficient and (F_{k}=F(x_{k})).

Maximization is achieved by solving the following subproblems sequentially.

We can achieve the two objectives by solving the two subproblems below sequentially.

The schemes may be understood in the context of a game in the following way: When the leader provides a decision (u^{k}=(x_{1}^{k},ldots,x_{m}^{k}, lambda^{k} )), all followers decide their strategies (tilde{x}_{i}^{k}) ((i=1,2,ldots,m)) simultaneously by solving the corresponding subproblems in (1.5), respectively.

From that value, the CDM starts by solving the dual subproblems in (10) in order to obtain y 0. As a result, there are two possibilities, namely, (i) ∑ j y j 0 ≤ C and (ii) ∑ j y j 0 > C. In the first situation, μ 0 as well as y 0 and the corresponding values in {x j } are optimal.

As the following theorem indicates, an optimal S-restricted candidate supertree can be found by solving the associated subproblems separately and combining their answers.

Thus, by solving the above subproblems iteratively for increasing k, each step can utilize the results from the previous steps (see [ 24]).

Based on the SC assignment (left ({delta _{k}^{l}}right)^) determined through solving the subproblem (mathcal {OP}_{2a}), the subproblem (mathcal {OP}_{2b}) can be solved by the dual method.