凸规划

Firstly, we characterize the strong no-arbitrage and weak no-arbitrage in terms of some convex programming problem.

首先利用一个凸规划刻画了无套利条件，并讨论了无套利条件与状态价格向量之间的关系。

Based on a new class equivalent condition of convex programming problems, which was first presented by Fischer, a new continuous method was put forward to solve the problem.

利用Fischer提出的一类新的凸规划问题等价条件，给出了一个解此问题新的连续化方法。

Based on Advanced Public Transportation System, the paper studies the vehicle dynamic dispatching problem of singular bus line. A real-time operational control model is developed to deal with the problem, which proves to be a convex programming.

基于先进公共交通系统环境，研究了城市公共汽车单线路运行系统的动态调度问题，建立了公交车辆运行的实时控制模型，证明其为凸规划问题。

Kun—Tucker condition is an effective way to deal with convex programming. So we based on this method to analysis the constraint model.

根据库恩——塔克条件解决凸规划问题的思想对模型进行分析，使得模糊需求报童问题更切实际。

Under some assumption conditions, we also developed trust region and affine scaling algorithm and potential reduction algorithm for convex programming problem with linear constraints.

然后在一定的假设条件下，对线性约束下的凸规划问题我们给出了相应的信赖域仿射尺度算法和势函数下降算法。

The module conversion for a kind of Max-min problems is given, namely, the Max-min problem with equality and inequality constraint is converted into convex problem with linear constraint, which provides theoretical basis for designing effective algorithms.

最后，给出一类极大极小问题的模型转化，把带等式、不等式约束的极大极小问题转化为带线性约束的凸规划问题，这为设计更为有效的算法提供了理论依据。

An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed.

对求解带有不等式约束的非线性非凸规划问题的一个精确增广Lagrange函数进行了研究。

We introduce convex,and in particular semidefinite,optimization methods,duality and complexity theory to shed new light to this relation for the single stock problem, given moments of the prices of the underlying assets,we show that we can find best possible bounds on option prices with general payoff funcations efficiently,either algorithmically(solving a semidefinite optimization problem)or in closed form, conversely,given observable option prices,we provide best possible bounds on moments of the prices of the underlying assets,as well as on the prices of the other options on the same asset by sovling linear optimization problems for options that are affected by multiple stocks either directly(the payoff of the option depends on multiple stocks)or indirectly(we have information on correlations between stock prices),we find on-optimal bounds using convex optimization methods,however,we show that it is NP-hard to find best possible bounds in multiple dimensions,we extend our results to incorporate transactions costs,this paper,in theory and practice can provide a reference to researchers and designers about Chinese financial derivative products,the full text is divided into six chapters as follows: ChapterⅠ:Papers on the background and significance of the subjects on a number of option pricing models as well as their advantages and shortcomings of the model and describes the status of research and writing papers and the main contents of the basic idea.

相应地，给定期权价格，也能够出标的资产瞬时价格的最有可能的最好的界。还有通过解决一个线性最优化问题，根据同一标的资产的其他期权的价格来找到这个期权的界值，对于期权受到多种股票价格直接影响(期权的收益依赖于多种股票)或者间接影响(我们有股票之间联系的有用信息)，如果使用凸规划方法我们就会发现没有最优的界，也能够证明对于多维情形确实是很难找到最优的最有可能的界值，最后将这一结论推广到考虑交易成本的情况。本文在理论和实践上给我国金融衍生产品研究者和设计者提供一定的参考。全文共分为六章，具体安排如下：第一章：阐述论文的选题背景和意义，介绍期权定价的一些模型以及这些模型的优点与缺点，并介绍国内外研究的现状以及论文的写作基本思路与主要内容。

Stochastic convex programming; Monte Carlo methods; Financial optimization; Convergence with probability one; Optimality condition; Monte Carlo penalty function methods; Nonsmooth optimization; Directional derivative; Subdifferential; Confident interval; Conditional Value-at-Risk; Optimal reinsurance

基础科学，数学，运筹学随机凸规划； Monte Carlo方法；金融优化；以概率1收敛；最优性条件； Monte Carlo罚函数法；非光滑优化；方向导数；次微分；置信区间；条件风险价值；最优再保险

In chapter 7, quality loss cost is first used in the model of simultaneous design of tolerance, and economically attainable accuracy of position is first considered as constraint condition. It is first proven that the function of simultaneous design of tolerance is non-convex program; discrete and continuos Simulated Annealing are introduced; the optimum software to solve this model is given.

第七章首次将质量损失成本用于公差并行设计的优化数学模型中，并首次考虑位置精度的经济加工精度范围作为约束条件；论证了公差并行设计优化模型的非凸规划问题；着重介绍了离散型和连续型的模拟退火算法SA；研制了公差并行设计的优化软件。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。