一阶条件方法的有效性及其求解分析

委托代理问题的一阶条件方法,是将代理人激励相容约束进行松弛处理,利用代理人效用函数的稳定点来代替最大化效用约束．这对于问题带来了数学处理上的方便, 但是一般情况下,这种方法是无效的．本文对于求解委托代理问题的一阶条件方法的背景,一阶条件方法的有效性,实用性进行了分析,并给出了其中一类问题的解决方法．     

一阶最优性条件研究

本对由Botsko的关于多变量函数取极值的一阶导数检验条件定理^[1]进行了分析研究，给出了更实用而简捷的差别条件。最后，举出若干例子予以说明。     

Hilbert空间中的一类双层规划问题的一阶与二阶最优性条件

本文考虑Hilbert空间中的,上层为有限个不等式约束,下层是一锥约束参数规划的双层规划问题的最优性条件.首先,利用下层问题最优值函数的方向导数的上下界的性质给出一阶最优性条件.之后,在使下层问题的最优值函数是二阶方向可微的条件下,证明了二阶必要性条件.     

一类广义半无限规划问题的一阶最优性条件

本文利用一个精确增广Lagrange函数研究了一类广义半无限极小极大规划问题。在一定的条件下将其转化为标准的半无限极小极大规划问题。研究了这两类问题的最优解和最优值之间的关系,利用这种关系和标准半无限极小极大规划问题的一阶最优性条件给出了这类广义半无限极小极大规划问题的一个新的一阶最优性条件。     

一阶常微分方程组周期边值问题的正解

利用锥上的不动点指数研究了一阶非线性常微分方程组的周期边值问题.在某些条件下,证明了上述周期边值问题正解的存在性.     

一类一阶周期边值问题解的存在性

考虑一类一阶常微分方程的周期边值问题,利用Schaefer不动点定理得到了边值问题解存在的一个充分条件,推广了相关文献中已有的结果.     

一阶双曲方程的Legendre—Tau方法

文章采用Legendre—tau方法对一阶双曲方程进行数值求解,此方法可以被有效实施,且可以得到L^2模意义下的最优误差估计,将以往对此类问题的收敛阶估计由O（N^1-τ）提高到O（N^-τ）,改进了原有的理论分析结果,数值算例证实了此方法的有效性．     

多期有限合伙制与公司制的道德风险和机制选择北大核心CSCD

本文基于委托代理理论和博弈论建立了有限合伙制与公司制下的多期道德风险模型,分析了委托人和代理人如何对这两种机制进行选择的问题．结论表明：两种机制下均存在道德风险问题,且在有限合伙制下因激励程度较高得到改善;两种机制相比较,公司制在特定条件下为博弈双方的最优选择,而有限合伙制只有在博弈双方地位不平等时才能达成．     

半无限规划的一阶最优性条件和牛顿型算法

在Fischer-Burmeister非线性互补函数的基础上,得到了半无限规划问题的一个新的一阶必要条件,并将半无限规划问题转化成一个光滑的无约束优化问题,给出了适合该问题的一个Damp-Newton算法,数值例子表明:算法结构简单,数值计算有效.     

双层规划的递阶交互决策有效化方法

本文讨论了协调集上双层规划问题解的性质,所得结论表明上层将所得利益全部让给下层,或下层将所得利益全部让给上层.当决策者不满足此种有效化方式时,必须寻找体现递阶结构的有效化方法.本文给出了一种保持递阶结构的递阶交互决策有效化方法.该方法适用于下层有多个平行子问题的双层线性规划.     

Innovation in long-term care insurance: Joint contracts for mitigating relational moral hazard

A recent innovation is joint long-term care (LTC) insurance policies covering two related individuals. This contribution purports to find out whether they have the potential of mitigating relational moral hazard (RMH) effects. Intra-family moral hazard has been suspected of being responsible for the sluggish development of private LTC insurance. The parent, anticipating the informal care provided by a family member LTC, is tempted to buy less LTC coverage. The family member (or more generally, the partner of a senior person), knowing that the bequest is protected by LTC insurance, has less incentive to provide informal care. Since a joint LTC policy makes senior and partner decide simultaneously rather than sequentially, it may lead to a partial internalization of RMH effects by turning coverage purchased by the senior and informal care provided by the partner from strategic substitutes into strategic complements under certain conditions.     

Interactive fuzzy goal programming approach for bilevel programming problem

This paper presents an interactive fuzzy goal programming (FGP) approach for bilevel programming problems with the characteristics of dynamic programming (DP).     

A dual-relax penalty function approach for solving nonlinear bilevel programming with linear lower level problem

The penalty function method, presented many years ago, is an important numerical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty function approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.     

A bilevel programming approach to the travelling salesman problem

We show that the travelling salesman problem is polynomially reducible to a bilevel toll optimization program. Based on natural bilevel programming techniques, we recover the lifted Miller-Tucker-Zemlin constraints. Next, we derive an O(n²) multi-commodity extension whose LP relaxation is comparable to the exponential formulation of Dantzig, Fulkerson and Johnson.     

Carbon tax based on the emission factor: a bilevel programming approach

We present a bilevel programming approach to design an effective carbon tax scheme based on the production emission factor, used as an intensity measure, for a competitive market with multiple players. At the upper level, the government sets a target emission factor for the industry and taxes firms if they exceed that target. At the lower level, the industry sets output levels that maximize social welfare. The bilevel model is transformed to a linear MIP by replacing the lower level optimization problem by its KKT conditions, and linearizing the complementarity slackness conditions. We test the model in the context of the cement industry. The results show that the proposed model finds the optimal tax rate that induces firms to switch to less carbon-intensive fuels and reduces the overall emissions.     

Characterizing optimal wages in principal-agent problems without using the first-order approach

The analysis of the principal-agent problem usually requires the classical first-order approach (FOA). However, the validity of the FOA makes restrictive assumptions on the problem under consideration such as the convexity of the distribution function condition. The main aim of this paper is to compute the optimal wages and characterize a closed form solution to the risk-neutral principal-agent problem with limited liability constraints. The development in this paper mainly invokes certain techniques in the semi-infinite programming rather than the FOA.     

A solution approach to the weak linear bilevel programming problems

In this paper, we study the weak linear bilevel programming problems. For such problems, under some conditions, we first conclude that there exists a solution which is a vertex of the constraint region. Based on the classical Kth-Best algorithm, we then present a solution approach. Finally, an illustrative example shows that the proposed approach is feasible.     

On bilevel programming,Part I: General nonlinear cases

This paper is concerned with general nonlinear nonconvex bilevel programming problems (BLPP). We derive necessary and sufficient conditions at a local solution and investigate the stability and sensitivity analysis at a local solution in the BLPP. We then explore an approach in which a bundle method is used in the upper-level problem with subgradient information from the lower-level problem. Two algorithms are proposed to solve the general nonlinear BLPP and are shown to converge to regular points of the BLPP under appropriate conditions. The theoretical analysis conducted in this paper seems to indicate that a sensitivity-based approach is rather promising for solving general nonlinear BLPP.This research is sponsored by the Office of Naval Research under contract N00014-89-J-1537.     

Finding an efficient solution to linear bilevel programming problem: An effective approach

Multilevel programming is developed to solve the decentralized problem in which decision makers (DMs) are often arranged within a hierarchical administrative structure. The linear bilevel programming (BLP) problem, i.e., a special case of multilevel programming problems with a two level structure, is a set of nested linear optimization problems over polyhedral set of constraints. Two DMs are located at the different hierarchical levels, both controlling one set of decision variables independently, with different and perhaps conflicting objective functions. One of the interesting features of the linear BLP problem is that its solution may not be Paretooptimal. There may exist a feasible solution where one or both levels may increase their objective values without decreasing the objective value of any level. The result from such a system may be economically inadmissible. If the decision makers of the two levels are willing to find an efficient compromise solution, we propose a solution procedure which can generate effcient solutions, without finding the optimal solution in advance. When the near-optimal solution of the BLP problem is used as the reference point for finding the efficient solution, the result can be easily found during the decision process.