Robust optimization with applications to game theory

In this article, we investigate robust optimization equilibria with two players, in which each player can neither evaluate his opponent's strategy nor his own cost matrix accurately while may estimate a bounded set of the strategy or cost matrix. We obtain a result that solving this equilibria can be formulated as solving a second-order cone complementarity problem under an ellipsoid uncertainty set or a mixed complementarity problem under a box uncertainty set. We present some numerical results to illustrate the behaviour of robust optimization equilibria.     

Second-order conditions in c1, 1 optimization with applications

Second-order necessary conditions for inequality and equality constrained C^{1, 1} optimization problems are derived. A constraint qualification condition which uses the recent generalized second-order directional derivative is employed to obtain these conditions. Various second-order sufficient conditions are given under appropriate conditions on the generalized second-order directional derivative in a neighborhood of a given point. An application of the secondorder conditions to a new class of nonsmooth C^{1, 1} optimization problems with infinitely many constraints is presented.     

氟硅酸化学沉淀法净化萃余酸中的镁

通过二次回归正交设计,实验研究了化学沉淀法净化未经浓缩的革余酸中镁离子的工艺条件,对氟硅酸用量、萃余酸水去除量、反应温度和反应时间四个因子进行了研究。实验结果表明:当氟硅酸用量为95.71g,除水量为80.41g,反应温度为36.02℃,反应时间为45.03min时,可使镁离子去除率达到最佳值,达到生产优等DAP的磷酸要求;实验得到的镁去除率(y)与氟硅酸用量(z_1)、除水量(z_2)、反应温度(z_3)和反应时间(z_4)的模型预测方程为:y= 59.1785-0.541156z_1+0.425071z_2-0.660951z_3-1.635317z_1²+1.768750z_1z_2-6.392974z_22+1.768750z_1z_2-6.392974z_2²+1.011250z_1z_3-0.978750z_2z_3-0.611140z_32+1.011250z_1z_3-0.978750z_2z_3-0.611140z_3²-1.106885z_42-1.106885z_4².     

非傍轴厄米-正弦-高斯光束的特性

为了研究厄米-正弦-高斯(HSiG)光束在非傍轴情形下受参量影响的特性,基于光强二阶矩理论,经过一系列复杂的数学计算,得出了非傍轴厄米-正弦-高斯光束的远场发散角、束腰宽度以及光束传输因子的解析式,并通过数值模拟,得到了它们与离心参量的关系。结果表明,在束腰宽度与波长比取值逐渐减小时,随着离心参量趋于0,当阶数为奇数和偶数时.发散角分别趋于63.435°和73.898°。束腰宽度和光束传输因子随参量的增加呈现较大的起伏,非傍轴情形下的光束传输因子取值与傍轴情况有很大的不同,其受参量影响不仅可以小于1,甚至趋于0。     

级联拉曼激光器的二阶近似解

利用非线性方法可以得到级联掺磷拉曼光纤激光器的二阶近似解.将描述抽运光和斯托克斯(Stokes)光沿光纤分布的微分方程组简化成代数方程组,在此基础上对抽运光采用二阶非线性近似得到了不同输入抽运功率情况下的近似解,并求出了在二阶非线性近似下的一级Stokes光和二级Stokes光的阈值表达式.利用得到的二阶近似解同一般的数值解法作比较,结果表明两者吻合得很好.一方面,对于双波长输出的级联掺磷拉曼光纤激光器,二阶方法比线性方法更加精确,更接近于一般的数值解;另一方面,该方法有效提高了数值运算速度,优于一般的数值方法.     

高阶色散效应常系数Ginzburg-Landau方程自相似脉冲演化的解析分析

采用自相似分析方法,基于常系数高阶色散的Ginzburg-Landau方程,通过分离变量法得出了高阶色散效应自相似脉冲演化的解析解,给出了自相似脉冲的振幅、相位、啁啾以及脉冲宽度的一般表达式.研究表明,在增益光纤的二阶正常色散区域,同时考虑高阶色散和增益色散双重效应影响下演化的自相似孤子脉冲仍然保持线性啁啾;振幅解析解的三阶色散效应显著.这与数值计算的结果非常一致. 关键词： 三阶色散 Ginzburg-Landau方程 自相似脉冲 二阶正常色散