Abstract We study distinguished objects in the category $\mathcal{B}\mathcal{L}$ of Banach lattices and lattice homomorphisms. The free construction introduced by de Pagter Wickstead [ 8] generates push-outs, combining this with an old result Kellerer 17] on marginal measures, amalgamation property is established. This will be key tool to prove that $L_1([0,1]^{\mathfrak{c}})$ separably $\mathc...

We present an Alternating Direction Method of Multipliers (ADMM) algorithm for solving optimization problems with an `1 regularized least-squares cost function subject to recursive equality constraints. The considered optimization problem has applications in control, for example in `1 regularized MPC. The ADMM algorithm is easy to implement, converges fast to a solution of moderate accuracy, an...

Let $X/\mathbb {F}_{q}$ be a smooth, geometrically connected, quasi-projective scheme. $\mathcal {E}$ semi-simple overconvergent $F$ -isocrystal on $X$ . Suppose that irreducible summands {E}_i$ of have rank 2, determinant $\bar {\mathbb {Q}}_p(-1)$ , and infinite monodromy at $\infty$ further for each closed point $x$ the characteristic polynomial is in $\mathbb {Q}[t]\subset \mathbb {Q}_p[t]$...