We consider the problem of minimizing sum two convex functions: one is differentiable and relatively smooth with respect to a reference function, other can be nondifferentiable but simple optimize. investigate triangle scaling property Bregman distance generated by function present accelerated proximal gradient (ABPG) methods that attain an $$O(k^{-\gamma })$$ convergence rate, where $$\gamma \...

The main purpose of this paper is to study the relationship between those functions that aggregate relaxed indistinguishability fuzzy relations with respect a collection t-norms and merge pseudo-metrics, extending classical approach explored for pseudo-metrics relations. Special attention paid distinguished class SSI-relaxed showing merging special type can be expressed through aggregating SSD-...

The Georgi-Machacek model, introducing a complex and real scalar triplet as additional components of the electroweak symmetry breaking sector, enables substantial contributions to weak gauge boson masses, subject equality vacuum expectation values (vev) via custodial SU(2) symmetry. We present an updated set constraints on this scenario, from collider data (including those 137/139~fb$^{-1}$ lum...

The notions of relaxed submonotone and relaxed monotone mappings in Banach spaces are introduced and many of their properties are investigated. For example, the Clarke subdifferential of a locally Lipschitz function in a separable Banach space is relaxed submonotone on a residual subset. For example, it is shown that this property need not be valid on the whole space. We prove, under certain hy...

We use the Margin Infused Relaxed Algorithm of Crammer et al. to add a large number of new features to two machine translation systems: the Hiero hierarchical phrasebased translation system and our syntax-based translation system. On a large-scale ChineseEnglish translation task, we obtain statistically significant improvements of +1.5 B and +1.1 B, respectively. We analyze the impact of ...

In this paper, we introduce the class of multivalued relaxed μ quasimonotone operators and establish the existence of solutions of variational inequalities for such operators. This result is compared with a recent result of Bai et al on densely relaxed pseudomonotone operators. A similar comparison regarding an existence result of Luc on densely pseudomonotone operators is provided. Also, we in...