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Rupture velocity and maximum slip were left relatively unconstrained (Vr = 1.25 3.25 km/s; maximum slip = 100 m), and moment minimization constraints were reduced, such that moment is controlled by the inverted data rather than by an assumed initial condition.
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For example, reference [15] used TV minimization constraint for cone beam CT reconstruction.
It usually contains a logarithmic barrier function and the Newton method for minimization without constraints [21].
Computation of chemical equilibria in multiphase systems by Gibbs free energy minimization under constraints set by the material balance has increasing interest in many application fields, including materials technology, metallurgy and chemical engineering.
Once found all distinct constrained minima [see the Supporting Information (S11) for one in perfect agreement with the experimental intensities], we then continued the energy minimization without constraints, by adjusting also the unit cell axes and angles.
Because many of these coefficients are correlated, we still need stabilize the inversions by applying the derivative minimization smooth constraint of fault slip (Ji et al., 2002), as well as a temporal constraint.
This index can be determined by several algorithms dealing with minimization under constraint such as the well known Rackwitz Fiessler algorithm based on the projection gradient method.
The formulation of the proposed RBTO is established as a volume minimization problem under constraints established within the possibility context, termed as failure possibility constraints.
Finally, we use the l1 minimization with relaxed constraints to reconstruct the original signal r ̄ ∗.
The approach is based on the least squares minimization with regularization constraints provided by the spectral properties of the operator.
Here in this paper, an attempt is made to achieve the dual goal of profit maximization and cost minimization within certain constraints.
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