仿射变换内点信赖域类方法解单调变分不等式问题

基于Taji引入的一类可微的简单边界约束的严格单调变分不等式问题的势函数,本文提出了仿射变换内点信赖域类修正牛顿法.进一步,作者不仅从理论上证明了该算法的整体收敛性,并且在合理的假设条件下,给出了算法具有局部二次收敛速率.     

GLOBAL CONVERGENCE OF A TRUST REGION ALGORITHM USING INEXACT GRADIENT FOR EQUALITY-CONSTRAINED OPTIMIZATION

1 IntroductionIn this papert we study following nonlinear equlity-constrained optimization problem,where C(x) = (of(x), c200,' t c.(x))"(m 5 n), f, ci: R" -- R are at least twice contimuouslydifferentiable, AC(~) has fllll column rank in the range of interest.There are many trust-region algorithms for problem (1.1), (see [11,[2],[5]), these papershave a same point that is using exact gradient informations, but it is in realistic application.[3] and [41 give a trust region algorithm using i…     

Inexact-Restoration Method with Lagrangian Tangent Decrease and New Merit Function for Nonlinear Programming

A new inexact-restoration method for nonlinear programming is introduced. The iteration of the main algorithm has two phases. In Phase 1, feasibility is improved explicitly; in Phase 2, optimality is improved on a tangent approximation of the constraints. Trust regions are used for reducing the step when the trial point is not good enough. The trust region is not centered in the current point, as in many nonlinear programming algorithms, but in the intermediate more feasible point. Therefore, in this semifeasible approach, the more feasible intermediate point is considered to be essentially better than the current point. This is the first method in which intermediate-point-centered trust regions are combined with the decrease of the Lagrangian in the tangent approximation to the constraints. The merit function used in this paper is also new: it consists of a convex combination of the Lagrangian and the nonsquared norm of the constraints. The Euclidean norm is used for simplicity, but other norms for measuring infeasibility are admissible. Global convergence theorems are proved, a theoretically justified algorithm for the first phase is introduced, and some numerical insight is given.     

基于博弈的网络团购供应链信任协调机制研究

随着网络团购的快速发展,失信问题日益突出,此问题若得不到解决,将严重制约网络团购的发展规模.分析了影响供应链成员间信任的因素,并在运用KMRW声誉模型进行有限次重复博弈的基础上,引入第三方信用监管机构,设计了相应的约束机制和激励机制.分析结果显示,声誉模型对交易双方信任合作提供隐性激励,建立长期战略合作关系,有利于机会主义的守约行为;第三方信用监管机构的介入可以约束交易双方的机会主义行为,减少他们之间的信息不对称,能够最大限度的减少网络团购交易中的风险.     

Exploring trust region method for the solution of logit-based stochastic user equilibrium problem

In this research paper, we explored using the trust region method to solve the logit-based SUE problem. We proposed a modified trust region Newton (MTRN) algorithm for this problem. When solving the trust region SUE subproblem, we showed that applying the well-known Steihaug-Toint method is inappropriate, since it may make the convergence rate of the major iteration very slow in the early stage of the computation. To overcome this drawback, a modified Steihaug-Toint method was proposed. We proved the convergence of our MTRN algorithm and showed its convergence rate is superlinear.     

网络直播对餐饮O2O外卖顾客信任的影响研究

网络直播是基于互联网快速发展的一种实时视讯方式,其内容真实不可篡改,具有良好的实证作用。餐饮O2O外卖是以互联网为媒介,顾客线上下单,享受线下送餐上门的一种餐饮模式。但近几年外卖食品安全问题频发,导致顾客信任下降。基于网络直播的属性,本文构建了网络直播对餐饮O2O外卖顾客信任影响的结构方程模型。并通过问卷调查,进行了实证研究。研究结果表明网络直播的内容、主体、方式、时间、次数均对顾客信任具有显著性正向影响。最后根据研究结果提出了提高餐饮O2O外卖顾客信任及发展网络直播模式的建议。     

广义几何规划的压缩共轭梯度路径非单调信赖域算法(英文)

In this paper,on the basis of making full use of the characteristics of unconstrained generalized geometric programming（GGP）,we establish a nonmonotonic trust region algorithm via the conjugate path for solving unconstrained GGP problem.A new type of condensation problem is presented,then a particular conjugate path is constructed for the problem,along which we get the approximate solution of the problem by nonmonotonic trust region algorithm,and further prove that the algorithm has global convergence and quadratic convergence properties.     

信赖域子问题使用重新开始策略的共轭梯度法

给出了用共轭梯度法解信赖域子问题的重新开始策略，并证明了方法的收敛性，数值结果表明该策略可以大大提高算法的收敛速度．     

Smoothing Trust Region Methods for Nonlinear Complementarity Problems with P 0-Functions

By using the Fischer–Burmeister function to reformulate the nonlinear complementarity problem (NCP) as a system of semismooth equations and using Kanzow’s smooth approximation function to construct the smooth operator, we propose a smoothing trust region algorithm for solving the NCP with P ₀ functions. We prove that every accumulation point of the sequence generated by the algorithm is a solution of the NCP. Under a nonsingularity condition, local Q-superlinear/Q-quadratic convergence of the algorithm is established without the strict complementarity condition. This work was partially supported by the Research Grant Council of Hong Kong and the National Natural Science Foundation of China (Grant 10171030).     

Superlinear convergence of a trust region-type successive linear programming method

The convergence rate of the SLP method suggested in Ref. 1 is discussed for composite nondifferentiable optimization problems. A superlinear rate is assured under a growth condition, and it is further strengthened to a quadratic rate if the inside function is twice differentiable. Several sufficient conditions are given which make the growth condition true. These conditions can be relaxed considerably in practical use.This research was supported in part by the National Natural Science Foundation of China.The author is grateful to Professor E. Sachs, Universität Trier, Trier, West Germany, for his helpful suggestions.