Backward–forward algorithms for structured monotone inclusions in Hilbert spaces

In this paper, we study the backward–forward algorithm as a splitting method to solve structured monotone inclusions, and convex minimization problems in Hilbert spaces. It has a natural link with the forward–backward algorithm and has the same computational complexity, since it involves the same basic blocks, but organized differently. Surprisingly enough, this kind of iteration arises when studying the time discretization of the regularized Newton method for maximally monotone operators. First, we show that these two methods enjoy remarkable involutive relations, which go far beyond the evident inversion of the order in which the forward and backward steps are applied. Next, we establish several convergence properties for both methods, some of which were unknown even for the forward–backward algorithm. This brings further insight into this well-known scheme. Finally, we specialize our results to structured convex minimization problems, the gradient-projection algorithms, and give a numerical illustration of theoretical interest.     

二阶积分微分方程的广义拟线性化方法

运用广义拟线性化方法研究了正规锥上的二阶积分微分方程初值问题,获得了逼近解序列一致且平方收敛的结果.     

Alternative formulations for the Set Packing Problem and their application to the Winner Determination Problem

An alternative formulation for the set packing problem in a higher dimension is presented. The addition of a new family of binary variables allows us to find new valid inequalities, some of which are shown to be facets of the polytope in the higher dimension. We also consider the Winner Determination Problem, which is equivalent to the set packing problem and whose special structure allows us to easily implement these valid inequalities in a very easy way. The computational experiments illustrate the performance of the valid inequalities and obtain good results.     

Arresting wave collapse by wave self-rectification

We put forward a mechanism for tailoring, and even arresting, the collapse of wave packets in nonlinear media, whose dynamics is governed by nonlocal two-dimensional nonlinear Schr?dinger-like equations. The key ingredient of the scheme is the self-generation of nonlocal nonlinearities mediated by wave rectification.     

The trace of totally positive algebraic integers

For all totally positive algebraic numbers except a finite number of explicit exceptions, the following inequality holds:

\max(1.780022,1.66+\alpha_1), \end{displaymath}">

where is the degree of and its conjugates. This improves previous results of Smyth, Flammang and Rhin.

     

逐步增加的Ⅱ型截尾下冷贮备串联系统可靠性指标的Bayes估计

在逐步增加的Ⅱ型截尾模型下,运用Bayes方法,研究部件寿命服从双参数指数分布的冷贮备串联系统可靠性指标的近似置信区间问题.在两个参数均未知的情形下,给出了失效率,系统可靠度及平均寿命的Bayes近似置信区间的计算公式;对于超参数的确定,给出一种新的方法;最后进行了随机模拟,并对近似置信区间的精度进行了讨论.     

A q-linear analogue of the plane wave expansion

We obtain a q-linear analogue of Gegenbauer?s expansion of the plane wave. It is expanded in terms of the little q-Gegenbauer polynomials and the third Jackson q-Bessel function. The result is obtained by using a method based on bilinear biorthogonal expansions.     

An optimal replenishment policy for an EOQ model with partial backlogging

We study an inventory system where demand on the stockout period is partially backlogged. The backlogged demand ratio is a mixture of two exponential functions. The shortage cost has two significant costs: the unit backorder cost (which includes a fixed cost and a cost proportional to the length of time for which the backorder exists) and the cost of lost sales. A general procedure to determine the optimal policy and the minimum inventory cost for all the parameter values is developed. This model generalizes several inventory systems analyzed by different authors. Numerical examples are used to illustrate the theoretical results.