最优化

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。

Our company adhere to the optimization of product mix the best price the best service to win the market.

本公司坚持以最优化的产品结构最好的价格最佳的服务来赢得市场。

In Chapter 5, the authors study the convergence properties of the gradient projection method for the constrained optimization problem. In this chapter, a new step-size rule, which avoids fulfiling the classical line search and includes choosing a constant as the step size as a special case, is presented and analyzed.

第五章研究了求解约束最优化问题的梯度投影方法，在步长的选取时采用了一种新的策略，这种策略不需要进行传统的线搜索且包含步长取常数这种特例，在较弱的条件下，证明了梯度投影方法的全局收敛性。

The projection gradient method will be a possible way to solve the problem that we just get. It has been shown that the projections of the every directions, of which is the boundary point in linear restraint problems, are the possible decent directions, and the projection of negative grads direction is a decent direction. In 1960, Rosen proposed the basic idea of projection gradient methods, and then lots of researchers have been tried to find the convergence of this method. But most of them get the convergence with the condition to amend the convergence itself.

在约束最优化问题的算法中怎样寻找有效的下降方向是构造算法的重要内容，在寻找下降方向方面可行方向法中的投影梯度法有效的解决了下降方向的寻找问题，利用线性约束问题边界点的任意方向在边界上的投影都是可行方向，而负梯度方向的投影就是一个下降方向。60年代初Rosen提出投影梯度法的基本思想，自从Rosen提出该方法以后，对它的收敛性问题不少人进行了研究，但一般都是对算法作出某些修正后才能证明其收敛的，直到最近对Rosen算法本身的收敛性的证明才予以解决。

Until recently, the convergence of the Rosen"s arithmetic has been proved. The projection gradient method is the generalization of Steepest decent method to constraint problem. So it does have a faster convergence speed that the fastest decent method . To solve the problem, many researchers have generalizat the well-developed optimization with unconstraint to the Rosen"s gradient method. The conjugate gradient method is one of success to solve the problem.

投影梯度法是最速下降法对约束问题的推广，因此没有较快的收敛速度，为了解决这个问题很多中外学者把发展得比较成熟的无约束最优化算法作类似的推广，其中共轭梯度方法是近年发展的很成熟的方法，它具有计算简单，算法结构好，计算量少，具有良好的收敛性等优点，而Rosen投影梯度法的提出使寻找下降方向变得简单。

By using the model of quadratic common rotation established between planting density, N, P, K and synthetic value of wood chemical components of Eucalyptus grandis Pulpwood, mutual-efficiency and optimization choice were done.

利用造林密度、氮、磷、钾肥与巨桉纸浆原料林木材化学成分综合分之间的通用二次旋转效应模型，进行了因素的交互效应分析以及最优化选择。

If we can put it all together and maximize this team, then nothing would surprise me.

如果我们能将这一切放在一起，最优化球队，那么没有什么会令我惊讶。

In this paper, a method of optimal parameter selection for determining two operating wavelengths and their bandwidths of a high precision noncontact dual wavelength fiber optic pyrometer is proposed.

对实用化的高精度非接触式双波长光纤高温计的工作波长及其带宽进行了最优化设计，获得了良好的效果。

Each of the results is analyzed and the optimum preparing technology is chosen. At last, the solid phase synthesis is determined as the best way to produce melamine pyrophosphate.

通过对以上每一试验结果的对比分析及最优化试验条件的选择，最终确定采用固相合成法作为焦磷酸三聚氰胺的合成方法。

In this paper, we show that when the data matrices are $2\times 2$ and $3\times 3$-dimensional, we can transfer the problem into an optimization problem with quadratic matrix inequality constraints, based on another equivalent robust optimization problem converted from the original one.

本文表明，当数据矩阵为2乘2阶，3乘3阶矩阵时，我们可以把上述问题转化成二次矩阵不等式约束的最优化问题。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新