Alternating direction method of multipliers (ADMM) is a popular first-order owing to its simplicity and efficiency. However, similar other proximal splitting methods, the performance ADMM degrades significantly when scale optimization problems solve becomes large. In this paper, we consider combining with class stochastic gradient variance reduction for solving large-scale non-convex non-smooth...

in this paper, the temperature distribution around a moving heat source had been investigated including the phase change and non phase change . in non-phase change state, the governing equation was converted to finite difference equation by finite volume method and the equation was solved by alternating direction implicit method. this method was unconditionally stable . in phase change state, t...

Beam shaping is becoming increasingly important for synchrotron X-ray applications. Although routine for visible light lasers, this is challenging for X-rays due to the limited source coherence and extreme optical tolerances required for the shaping mirrors. In deliberate defocusing, even surface errors <5 nm r.m.s. introduce damagingly large striations into the reflected beam. To counteract su...

We prove a relation in the algebra of the Jones Vassiliev invariants, giving a new restriction to the values of the Jones polynomial on knots, and the non-existence of another family of such relations. We prove, that Jones polynomials of positive knots have non-negative minimal degree and extend this result to k-almost positive knots. We prove that if a positive knot is alternating, then all it...

In this paper, the difference between the Alternating Direction Method (ADM) and the Non-Splitting Method (NSM) is investigated, while both methods applied to the simulations for 2-D multimaterial radiation diffusion issues. Although the ADM have the same accuracy orders with the NSM on the uniform meshes, the accuracy of ADM will decrease on the distorted meshes or the boundary of domain. Nume...

We introduce a new class of automata on infinite trees called alternating nonzero automata, which extends the class of non-deterministic nonzero automata. We reduce the emptiness problem for alternating nonzero automata to the same problem for non-deterministic ones, which implies decidability. We obtain as a corollary algorithms for the satisfiability of a probabilistic temporal logic extendin...