Let Ω and C be nonempty, closed and convex sets in R <Superscript> n </Superscript> and R <Superscript> m </Superscript> respectively and A be an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${m \times n}$$</EquationSource> </InlineEquation> real matrix. The split feasibility problem is to find <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${u \in \Omega}$$</EquationSource> </InlineEquation> with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$${Au \in C.}$$</EquationSource> </InlineEquation> Many problems arising in the image reconstruction can be formulated in this form. In...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></superscript></superscript>

We investigate in this paper the duality gap between quadratic knapsack problem and its Lagrangian dual or semidefinite programming relaxation. We characterize the duality gap by a distance measure from set {0, 1}<Superscript> n </Superscript> to certain polyhedral set and demonstrate that the duality gap can be reduced...</superscript>

The stochastic pooling problem is a type of stochastic mixed-integer bilinear program arising in the integrated design and operation of various important industrial networks, such as gasoline blending, natural gas production and transportation, water treatment, etc. This paper presents a...

In this paper, we introduce an iterative process which converges strongly to a common solution of finite family of variational inequality problems for γ-inverse strongly monotone mappings and fixed point of two continuous quasi-<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\phi}$$</EquationSource> </InlineEquation>-asymptotically nonexpansive mappings in Banach spaces....</equationsource></inlineequation>

Multidimensional scaling is a technique for exploratory analysis of multidimensional data. The essential part of the technique is minimization of a multimodal function with unfavorable properties like invariants and non-differentiability. Recently a branch and bound algorithm for...

The primary aim of this article is to resolve a global optimization problem in the setting of a partially ordered set that is equipped with a metric. Indeed, given non-empty subsets A and B of a partially ordered set that is endowed with a metric, and a non-self mapping <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${S : A \longrightarrow...</equationsource></inlineequation>