Generalized Bregman Projections in Convex Feasibility Problems

We present a method for finding common points of finitely many closed convex sets in Euclidean space. The Bregman extension of the classical method of cyclic orthogonal projections employs nonorthogonal projections induced by a convex Bregman function, whereas the Bauschke and Borwein method uses Bregman/Legendre functions. Our method works with generalized Bregman functions (B-functions) and inexact projections, which are easier to compute than the exact ones employed in other methods. We also discuss subgradient algorithms with Bregman projections.     

Linear and strong convergence of algorithms involving averaged nonexpansive operators

We introduce regularity notions for averaged nonexpansive operators. Combined with regularity notions of their fixed point sets, we obtain linear and strong convergence results for quasicyclic, cyclic, and random iterations. New convergence results on the Borwein–Tam method (BTM) and on the cyclically anchored Douglas–Rachford algorithm (CADRA) are also presented. Finally, we provide a numerical comparison of BTM, CADRA and the classical method of cyclic projections for solving convex feasibility problems.     

Feasibility study for the measurement of Bc meson mass and lifetime with the general purpose detector at the LHC

In this paper a feasibility study of the Bc meson to measure its mass and lifetime is described with the general purpose detector at the LHC.The study solely concentrated on the J/Ψπ+,J/Ψ→μ+μ- decay channel of the Bc and it was concluded that about 120 events can be selected in the first fb-1 of data.With this data sample,the mass resolution was estimated to be 2.0(stat.) MeV/c2 while the cr resolution was found to be 13.1(stat.) μm,I.e.the lifetime resolution to be 0.044(stat.) ps.     

基于FCE的建设项目环境效益可研指标的应用——以高速公路建设项目为例

应用FCE进行建设项目环境效益可研指标体系综合评价是一条科学精简的途径.高速公路建设项目对项目沿线环境的影响典型而尖锐,以高速公路建设项目为例分析FCE在建设项目环境效益可研指标中的应用,并以福银高速公路一期工程尤溪段施工期环境效益可研为例建立应用模型.     

Feasibility of home-away-pattern sets for round robin tournaments

A Home-Away-Pattern (HAP) set defines each team’s venue in each period. We consider the decision problem of whether a round robin tournament can be arranged on the basis of a given HAP set. We give a necessary condition which can be checked in polynomial time and conjecture it to be sufficient.     

Convergence in norm of modified Krasnoselski-Mann iterations for fixed points of demicontractive mappings

This paper deals with fixed points methods related to the general class of demicontractive mappings (including the well-known classes of nonexpansive and quasi-nonexpansive mappings) in Hilbert spaces. Specifically, we point out some historical aspects concerning the concept of demicontactivity and we investigate a regularized variant of the Krasnoselski-Mann iteration that can be alternatively regarded as a simplified form of the inertial iteration (P-E. Maingé, J. Math. Anal. Appl. 344 (2008) 876-887) with non-constant relaxation factors. These two methods ensure the strong convergence of the generated sequence towards the least norm element of the set of fixed-points of demicontractive mappings. However, for convergence, our method does not require anymore the knowledge of some constant related to the involved demicontractive operator. A new and simpler proof is also proposed for its convergence even when involving non-constant relaxation factors. We point out the simplicity of this algorithm (at least from computational point of view) in comparison with other existing methods. We also present some numerical experiments concerning a convex feasibility problem, experiments that emphasize the characteristics of the considered algorithm comparing with a classical cyclic projection-type iteration.     

Bi-extrapolated subgradient projection algorithm for solving multiple-sets split feasibility problem

This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.     

A non-interior continuation algorithm for solving the convex feasibility problem

In this paper, a specific class of convex feasibility problems are considered and a non-interior continuation algorithm based on a smoothing function to solve this class of problems is introduced. The proposed algorithm solves at most one system of linear equations at each iteration. Under some weak assumptions, we show that the algorithm is globally linearly and locally quadratically convergent. Preliminary numerical results are also reported, which verify the favorable theoretical properties of the proposed algorithm.     

Letter to the editor

It is shown that the recent characterization of strong feasibility of interval linear equations by Karademir and Prokopyev was in fact published by this author 13 years earlier. The original result was difficult to discover, having been embedded, together with its proof, into the proof of another theorem.