We discuss generalized proximity operators (GPO) and their associated generalized projection problems. On inputs of size n, we show how to efficiently apply GPOs and generalized projections for separable norms and distance-like functions to accuracy in O(n log(1/ )) time. We also derive projection algorithms that run theoretically in O(n log n log(1/ )) time but can for suitable parameter range...

Combining the techniques of the working set identification and generalized gradient projection, we present a new generalized gradient projection algorithm for minimax optimization problems with inequality constraints. In this paper, we propose a new optimal identification function, from which we provide a new working set. At each iteration, the improved search direction is generated by only one...

The approximate solvability of a generalized system for nonlinear variational inequality in Hilbert spaces was studied, based on the convergence of projection methods. But little research was done in Banach space. The primary reason was that projection mapping lacked preferably property in Banach space. In this paper, we introduced the generalized projection methods. By using these methods, the...

Very recently, a solution to the kernel-based online classification problem has been given by the adaptive projected subgradient method (APSM). The developed algorithm can be considered as a generalization of a kernel affine projection algorithm (APA) and the kernel normalized least mean squares (NLMS). Furthermore, sparsification of the resulting kernel series expansion was achieved by imposin...

The problem of reconstructing a measurable plane set from its two generalized projections is considered. It means that the projections contain also the effect of a known modification given in the whole plane. This is a more general case than that of a constant absorption within a given material. Via a suitable mapping, this generalized problem can be transformed into the solved case of the clas...

The panel on ‘Modeling of Multiphase Flow’ was convened by the first author (AP) and held on Monday, May 28. It was attended by well over 100 participants and the discussion could have easily gone on far beyond the 1 hr 40 mins allocated. Prof. Gad Hetsroni (Department of Mechanical Engineering, Technion, Haifa 32000, Israel) had to cancel his participation due to a last-minute commitment. The ...

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...