Sentence examples for using the convex optimization from inspiring English sources

The same scenarios are also investigated with the optimal solution using the convex optimization toolbox CVX in MATLAB [29].

We show that the corresponding optimization problems can be formulated as GP and thus optimal power allocation (OPA) can be obtained using the convex optimization techniques.

We propose an algorithm to divide the design problem into three subproblems, which can be solved using the convex optimization methods.

The H∞ fuzzy robust control design problem is parameterized in terms of a linear matrix inequality (LMI) problem, and the LMI problem can be solved very efficiently using the convex optimization techniques.

The sufficient conditions of ensuring the switched fuzzy control system asymptotic stabilization are proposed and parameterized in terms of linear matrix inequalities (LMIs), which can be solved very efficiently using the convex optimization techniques.

By considering a fuzzy Lyapunov function and by introducing slack variables, we propose the new sufficient stabilization conditions formulated in LMI constraints which can be easily solved using the convex optimization tools.

Using this definition, the (convex) optimization problem we have to solve in order to obtain our upper bound (at node l) is given by F U = max λ ∑ m = 1 M ∑ i = 1 I m log ∑ j = 1 J f ~ ij m ( P ̂ ) − ∑ v = 1 V λ v g ( P ̂ v ) s.t.

By plugging (5) and (9) into (18) and using the standard convex optimization techniques and the KKT conditions, the optimal solution of W to problem (17) is given by boldsymbol{W}_{j,k}=varpi_{j,k}sqrt{rho_{j,k}}boldsymbol{Phi}_{j}^{-1}boldsymbol{H}_{j,j,k}^{H}boldsymbol{U}_{j,k}^{H}boldsymbol{Sigma}_{j,k} (20).

Therefore, the optimal Lagrange multipliers of μ ∗ and λ ∗, in which maximize d, can be obtained by using the standard convex optimization techniques [23].

The water-filling algorithm is used to solve the convex optimization problem by considering a continuous objective function.

In this case, μpost and σ post 2 should be used to formulate the convex optimization problems shown in (11) and (18).