如果你也在 怎样代写优化方法Optimization这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。优化方法Optimization又称优化）或数学编程是指从一组可用的备选方案中选择一个最佳元素。从计算机科学和工程[到运筹学和经济学的所有定量学科中都会出现各种优化问题，几个世纪以来，数学界一直在关注解决方法的发展。
优化方法Optimization在最简单的情况下，优化问题包括通过系统地从一个允许的集合中选择输入值并计算出函数的值来最大化或最小化一个实际函数。将优化理论和技术推广到其他形式，构成了应用数学的一个大领域。更一般地说，优化包括在给定的域（或输入）中寻找一些目标函数的 “最佳可用 “值，包括各种不同类型的目标函数和不同类型的域。非凸全局优化的一般问题是NP-完备的，可接受的深层局部最小值是用遗传算法（GA）、粒子群优化（PSO）和模拟退火（SA）等启发式方法来寻找的。
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我们提供的优化方法Optimization及其相关学科的代写，服务范围广, 其中包括但不限于:
调和函数 harmonic function
椭圆方程 elliptic equation
抛物方程 Parabolic equation
双曲方程 Hyperbolic equation
非线性方法 nonlinear method
变分法 Calculus of Variations
几何分析 geometric analysis
偏微分方程数值解 Numerical solution of partial differential equations
数学代写|优化方法作业代写Optimization代考|Computation of Structural Reliabilities and its Sensitivities
The computation of reliabilities of mechanical structures is a well established method, see e.g. $[18,19,28,48]$. In the following we examine the potential of this technique to yield also the corresponding sensitivities, i.e. the derivatives of the probabilities of survival with respect to certain design variables or deterministic system parameters $x_{k}$.
According to $(3.22 a)$ and $(3.23 a)$ the probability function $D_{(0)} P(x):=$ $P(x)$ and its partial derivative $D_{(k)} P(x):=\frac{\partial P}{\partial x_{k}}(x)$ can jointly be represented by the formula
$$
D_{(l)} P(x)=\int_{\tilde{B}} c_{l}\left(q_{1}, q_{2} ; x\right) f_{1}\left(q_{1}\right) d q_{1} d q_{2}, l=0,1, \ldots, r .
$$
数学代写|优化方法作业代写Optimization代考|Numerical Computation of Derivatives of the Probability Functions Arising in Chance Constrained Programming
The technique of asymptotic expansion of integrals applied in Section $3.5 .1$ to the computation of reliabilities and its sensitivities of mechanical structures is considered now for the computation of the probability functions and its derivatives treated in Section 3.2.
For simplification, in the following we assume that $x_{j} \neq 0$ for all $j=$ $1,2, \ldots, r$. Hence, using transformation (3.10a’), corresponding to representations (3.10b) of $D_{(0)} P:=P$ and (3.13a) of $D_{(k)} P:=\frac{\partial P}{\partial x_{k}}, k \geq 1$, for $D_{(l)} P, l=0,1, \ldots, r$, we have the joint representation
$$
D_{(l)} P(x)=\int_{\sum_{j=1}^{r} q_{j} \leq q_{r+1}} h_{l}\left(q_{1}, \ldots, q_{r}, q_{s+1} ; x\right) \prod_{j=1}^{r+1} d q_{j}
$$
where $h_{0}$ is the integrand corresponding to ( $\left.3.10 \mathrm{~b}\right)$ for $l=0$; and for $l=k \geq 1$, the function $h_{k}$ is defined by a modification of (3.12b) based on (3.10a’).
Following now the integral transformation (3.37), we consider the transformation
$$
q_{j}:=\xi_{j}^{0} a_{j}, j=1, \ldots, r, q_{r+1}:=b
$$
with a fixed vector $\xi^{0}:=\left(\xi_{1}^{0}, \ldots, \xi_{r}^{0}\right)^{T}$ such that $\xi_{j}^{0} \neq 0$ for all $j=1, \ldots, r$. Applying (3.46) to the integral (3.45), for $l=0,1, \ldots, r$ we find
$$
\begin{aligned}
D_{(l)} P(x) &=\int_{A \xi^{0} \leq b} C_{l}(A, b ; x) f(A, b) d A d b \
&=E 1_{\left[A \xi^{0} \leq b\right]}(A(\omega), b(\omega)) C_{l}(A(\omega), b(\omega) ; x)
\end{aligned}
$$
where
$$
C_{l}(A, b ; x):=h_{l}\left(\xi_{1}^{0} a_{1}, \ldots, \xi_{r}^{0} a_{r}, b ; x\right) \frac{1}{f(A, b)} \prod_{j=1}^{r}\left|\xi_{j}^{0}\right|^{m}
$$
and $1_{\left[A \xi^{0} \leq b\right]}$ denotes the characteristic function of the set $\left[A \xi^{0} \leq b\right]:=$ $\left{(A, b) \in \mathbb{R}^{m(r+1)}: A \xi^{0} \leq b\right}$. Note that in $(3.47 \mathrm{a}, \mathrm{b})$ we have now again a fixed region of integration, cf. (3.22a,b). Furthermore, we observe that (3.47a) contains a mean value representation of $D_{(l)} P(x)$.
优化方法代写
数学代写|优化方法作业代写OPTIMIZATION代考|COMPUTATION OF STRUCTURAL RELIABILITIES AND ITS SENSITIVITIES
机械结构的可靠性计算是一种成熟的方法，参见例如[18,19,28,48]. 在下文中，我们研究了这种技术产生相应敏感性的潜力，即生存概率相对于某些设计变量或确定性系统参数的导数Xķ.
根据(3.22一种)和(3.23一种)概率函数D(0)磷(X):= 磷(X)及其偏导数D(ķ)磷(X):=∂磷∂Xķ(X)可以用公式联合表示
D(l)磷(X)=∫乙~Cl(q1,q2;X)F1(q1)dq1dq2,l=0,1,…,r.
数学代写|优化方法作业代写OPTIMIZATION代考|NUMERICAL COMPUTATION OF DERIVATIVES OF THE PROBABILITY FUNCTIONS ARISING IN CHANCE CONSTRAINED PROGRAMMING
节中应用的积分渐近展开技术3.5.1现在考虑计算机械结构的可靠性及其敏感性，以计算第 3.2 节中处理的概率函数及其导数。
为简化起见，下面我们假设$x_{j} \neq 0$ for all $j=$ $1,2, \ldots, r$. Hence, using transformation (3.10a’), corresponding to representations (3.10b) of $D_{(0)} P:=P$ and (3.13a) of $D_{(k)} P:=\frac{\partial P}{\partial x_{k}}, k \geq 1$, for $D_{(l)} P, l=0,1, \ldots, r$, we have the joint representation
$$
D_{(l)} P(x)=\int_{\sum_{j=1}^{r} q_{j} \leq q_{r+1}} h_{l}\left(q_{1}, \ldots, q_{r}, q_{s+1} ; x\right) \prod_{j=1}^{r+1} d q_{j}
$$
where $h_{0}$ is the integrand corresponding to ( $\left.3.10 \mathrm{~b}\right)$ for $l=0$; and for $l=k \geq 1$, the function $h_{k}$ is defined by a modification of (3.12b) based on (3.10a’).
Following now the integral transformation (3.37), we consider the transformation
$$
q_{j}:=\xi_{j}^{0} a_{j}, j=1, \ldots, r, q_{r+1}:=b
$$
with a fixed vector $\xi^{0}:=\left(\xi_{1}^{0}, \ldots, \xi_{r}^{0}\right)^{T}$ such that $\xi_{j}^{0} \neq 0$ for all $j=1, \ldots, r$. Applying (3.46) to the integral (3.45), for $l=0,1, \ldots, r$ we find
$$
\begin{aligned}
D_{(l)} P(x) &=\int_{A \xi^{0} \leq b} C_{l}(A, b ; x) f(A, b) d A d b \
&=E 1_{\left[A \xi^{0} \leq b\right]}(A(\omega), b(\omega)) C_{l}(A(\omega), b(\omega) ; x)
\end{aligned}
$$
where
$$
C_{l}(A, b ; x):=h_{l}\left(\xi_{1}^{0} a_{1}, \ldots, \xi_{r}^{0} a_{r}, b ; x\right) \frac{1}{f(A, b)} \prod_{j=1}^{r}\left|\xi_{j}^{0}\right|^{m}
$$
and $1_{\left[A \xi^{0} \leq b\right]}$ denotes the characteristic function of the set $\left[A \xi^{0} \leq b\right]:=$ $\left{(A, b) \in \mathbb{R}^{m(r+1)}: A \xi^{0} \leq b\right}$. Note that in $(3.47 \mathrm{a}, \mathrm{b})$ we have now again a fixed region of integration, cf. (3.22a,b). Furthermore, we observe that (3.47a) contains a mean value representation of $D_{(l)} P(x)$.
数学代写|优化方法作业代写Optimization代考 请认准UprivateTA™. UprivateTA™为您的留学生涯保驾护航。
