So, the above problem (8) can be solved by Augmented Lagrangian method as {begin{aligned} min_{u,p}max_{chi}{L_{rof} u,p,chi)}&=int_{Omega}|p|+frac{lambda}{2}||u-z||^{2}_{2} &quad+int_{Omega}chi. p-nabla u)+frac{r}{2}int_{Omega}|p-nabla u|^{2}, end{aligned}} (9). p-nabla
which can be solved by employing the alternating direction augmented Lagrange multiplier (ADALM) method, which is a simple, but powerful, algorithm that is well suited to large-scale optimization problems [28, 49].
This problem can be solved by ALM method which minimizes the following augmented Lagrange function: (18) || J || ∗ + || S || ∗ + λ || E || 1 + tr (Y 1 T (X − X Z − L X − E ) ) + tr (Y 2 T (Z − J ) ) + tr (Y 3 T (L − S ) ) + μ 2 (|| X − X Z − L X − E || F 2 + || Z − J || F 2 + || L − S || F 2 ), where tr and ||·|| F denote the trace and Frobenius norm of a matrix, respectively.
It has been previously demonstrated in [1, 2] that PST can be solved by several sparse recovery algorithms that fall into different categories, including augmented Lagrangian rank-minimization [1], ℓ 1 optimization approaches and probability-based methods [2].
It will be solved by psychologists".
Therefore, they can be solved by man.
It can be solved by political will.
The nonlinear differential-algebraic equations resulting from the finite element discretization are solved by Newton's method augmented with a pseudo-arc-length continuation scheme for tracing ignition and extinction points.
The findings are based on the total energy calculations where the Khon Sham (KS) equation is solved by means of an ab-initio full-potential linearized augmented plane wave (FP-LAPW) method.
The governing equations are the nonlinear Navier Stokes equations, augmented by an evolution equation for a passive scalar, which are solved by a spectral Fourier-based method.
