The purpose of this paper is using Korpelevich’s extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. Under suitable conditions, some existence theorems and approxima...

In this paper, we use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our method includes the two-step forward-backward splitting and extragradient methods for solving various cl...

In this paper, we suggest a hybrid method for finding a common element of the set of solution of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known methods: extragradient method and CQ method. We derive a necessary and sufficient condition f...

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 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 ...