… regularization parameter ℓ α were analyzed in order to evaluate its effects on the results of
the behavior curves and the crack paths in composites … to solve the optimization problem, and …

… stable for solving nonlinear optimization problems, and with the … as $\boldsymbol{Q} = \left\{\boldsymbol{x}
\ |\ \boldsymbol{A}_… However, direct implementation of Newton's method is not …

… To recover the shape of the boundary of Γ, we now consider the optimization problem (4).
To … relies on the Gauss-Newton method as a nonlinear iteration. Given a guess $q^{(j-1)}$ …

… from the statistics of the noise ${\boldsymbol \epsilon }$ … solve inequality-constrained
optimization problems, a barrier function … In this paper, we focus on the cases when the composite …

… \rightarrow D_{s}\), composite relaxations of h provide a means to … the factorable representation
of \(\boldsymbol{\ell}\), and hence … Newton method called the interval Hansen-Sengupta …

… In some applications we prefer a prior that allows less regularity… matrix Q for the prior;
typically, C is the Cholesky factor of Q . … form $\boldsymbol{y} = \boldsymbol{A}(\boldsymbol{x})$ …

… inverse mapping \(\boldsymbol{x}=g\left( \boldsymbol{y}\right… To reach the first goal, we
form an optimization problem to … To enable complete coupling of all dimensions, we composite …

… K$| subsets, solves the optimization problem using each subset, … Medicare patients by
fitting regularized Cox models with (i) |$p=… efficient procedure to estimate |$\boldsymbol{\beta}_0$| …

… algorithm, which does not require the specification of the posterior distribution. Moreover,
we discuss how to select the regularization … , \(\boldsymbol {Z}^\top _{ij}\) is a q × 1 vector of …

… macroscopic properties of a composite material from the … that no regularization of the
optimization problem is needed … {\chi}}_{\boldsymbol{T}}} \) enters the flow adjoint problem as …