We first investigate strong convergence of the sequence generated by implicit and explicit viscosity approximation methods for a one-parameter nonexpansive semigroup in a real Banach space E which has a uniformly Gâteaux differentiable norm and admits the duality mapping j <Subscript> φ </Subscript>, where φ is a...</subscript>

In this paper we apply two convexification procedures to the Lagrangian of a nonconvex semi-infinite programming problem. Under the reduction approach it is shown that, locally around a local minimizer, this problem can be transformed equivalently in such a way that the transformed Lagrangian...

We introduce a hybrid method for finding a common element in the solutions set of an equilibrium problem and the common fixed points set of a countable family of relatively quasi-nonexpansive mappings in a Banach space. A strong convergence theorem of the proposed method is established by using...

Recent studies on the kernel function-based primal-dual interior-point algorithms indicate that a kernel function not only represents a measure of the distance between the iteration and the central path, but also plays a critical role in improving the computational complexity of an...

In this paper we consider the contraction-proximal point algorithm: <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${x_{n+1}=\alpha_nu+\lambda_nx_n+\gamma_nJ_{\beta_n}x_n,}$$< /EquationSource> </InlineEquation> where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${J_{\beta_n}}$$</EquationSource> </InlineEquation> denotes the resolvent of a monotone operator A. Under the assumption that lim<Subscript> n </Subscript> α <Subscript> n </Subscript> = 0, ∑<Subscript> n </Subscript> α <Subscript> n </Subscript> = ∞, lim inf<Subscript> n </Subscript> β <Subscript> n...</subscript></subscript></subscript></subscript></subscript></subscript></equationsource></inlineequation></equationsource></inlineequation>

Given non-empty subsets A and B of a metric space, let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${S{:}A{\longrightarrow} B}$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${T {:}A{\longrightarrow} B}$$</EquationSource> </InlineEquation> be non-self mappings. Due to the fact that S and T are non-self mappings, the equations Sx=x and Tx=x are likely to have no common solution, known as a common fixed point...</equationsource></inlineequation></equationsource></inlineequation>

The minimum weighted dominating set (MWDS) problem is one of the classic NP-hard optimization problems in graph theory with applications in many fields such as wireless communication networks. MWDS in general graphs has been showed not to have polynomial-time constant-approximation if <InlineEquation ID="IEq1"> <EquationSource...</equationsource></inlineequation>

This paper presents a Branch, Bound, and Remember (BB&R) exact algorithm using the Cyclic Best First Search (CBFS) exploration strategy for solving the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${1|ST_{sd}|\sum T_{i}}$$</EquationSource> </InlineEquation> scheduling problem, a single machine scheduling problem with sequence dependent setup times where the objective is...</equationsource></inlineequation>