凹函数

In order to overcome the nonsmoothness of the objective function, we usea smoothed concave function to approximate the objective function.

为了易于求解该模型，本章采用一个光滑的凹函数来近似目标函数。

Assume that the transaction cost funaction is a convex function and the tax function is a concave funcatioh.

我们假设交易费用是交易金额的一个凸函数，而缴纳的税费是其收入的一个凹函数。

This paper discusses a variation equation problem in a class of singular stochastic control with stopping time,gives its solution under two different conditions,which is a one order continuous differentiable and concave function,and gives the exact form.

讨论了一类带停时的奇异型随机控制问题中的一个变分方程问题，并且在两种不同的情况下给出了该变分方程的解，即为一阶连续可导凹函数，并在两种情况下给出了此函数的具体形式。

Under these assumptions, for any given selling price the paper develops the criterion for the optimal solution to the replenishment schedule, and proves that the optimal replenishment policy not only exists but is also unique. It shows that the total profit per unit time is a concave function of price when the replenishment schedule is given.

在这些假设下，证明了对任意给定的价格，最优订货周期长度和该订货周期内最优存货时间的长度不但存在而且惟一，又证明了在给定订货周期条件下平均利润函数是关于价格的严格凹函数，求出了物品的最优销售价格。

Finally, the optimization warehousing allocation policy is achieved by digital simulation, which shows that expecting revenue is concave function of surplus capacity, and is also concave function of booking leading time, the opportunity costs is a non-increase function of surplus capacity, and is also is a non- increase function of booking leading time.

论文按照随机背包问题思路建立了考虑第三方仓储能力分配动态随机规划模型，对模型性质进行了分析，得到了基于阈值的舱位预订动态控制策略，并通过数值仿真，得知期望收益是剩余仓储能力的凹函数，是时间的凹函数；机会成本是剩余仓储能力的非增函数，是时间的非增函数。

The experimental results show that for most continuous optimization problems, the strategy of concave function gains an advantage over the linear strategy, while the linear strategy outperforms strategy of convex function with the identical initial and final weights.

试验结果表明，对于多数连续优化问题，在初始权值和最终权值相同的情况下，凹函数递减策略优于线性策略，而线性策略优于凸函数策略，凹函数递减策略能够在不影响收敛精度的情况下较大幅度地提高粒子群算法的收敛速度。

With the concave transaction cost function more conforming to the actual situation, we introduce condition risk value to measure profolio risk, and propose mean- CVaR concave integer programming model under concave transaction costs and minimal transaction unit constraints.

1取交易费用函数为更实际的凹函数，引入条件风险价值度量组合风险，提出了考虑交易费用及最小交易量的均值—CVaR凹整数规划模型。

Properties of efficient portfolios and the efficient frontier to the model are systematically analyzed. Our main results concerning the properties are: every efficient portfolio can be solved by minimizing portfolio risk under a given level of portfolio return or by maximizing portfolio return under a given level of portfolio risk; on the efficient frontier, the risk is a convex and strictly increasing function of the return and the return is a concave and strictly increasing function of the risk; the utility function on the efficient frontier can be expressed as a quasi-concave function of the risk or the return if the investor's utility function is quasi-concave.

从理论上系统地对该模型下的有效投资组合和有效前沿的性质进行了分析，结果表明：每一个有效投资组合可通过在给定期望收益水平的条件下最小化投资组合风险来获得，或者在给定风险水平的条件下最大化期望投资组合收益来获得；在有效前沿上，风险是收益的严格单调递增凸函数，收益是风险的严格单调递增凹函数；当投资者的效用函数是拟凹函数时，则有效前沿上的效用可表达成风险或收益的拟凹函数。

The convex function develeped so many years that convex functionals are now a class of very universal functionals.The kinetic energy in the classical is the most natural convex function.Others like entropy and so on are convex functions.The economic core is closely connected with the convex function.The western economic core question is the optimized question.The optimized theory has something to do with the convex function and the concave function.

凸函数的发展经年已相当完善其应用非常广泛，在古典力学中的动能，就是最自然直接的凸函数，其他如熵……等均是，连经济学的核心都与之有极密切相关，西方经济学的核心问题是最优化问题，最优化理论又与凸函数与凹函数密切相关。

The Mean-CVaR (Conditional Value-at-Risk) portfolio optimization model is proposed to calculate a globally optimal portfolio under concave transaction costs. A non-decreasing concave function is employed to approximate origin transaction costs function.

研究了当投资组合的风险用条件风险价值（Conditional Value at Risk，简称CVaR）度量，考虑凹交易费用的投资组合选择问题，通过对交易费用采用非线性的凹函数，建立了一个均值-CVaR模型。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了