S

Three types of material:

for  of the World Annual Energy Consumption

xT∇2L(x∗)x>0,,∀x∈C

C={x≠0:∇gi(x∗)Tx∇gi(x∗)Tx∇hi(x∗)Tx=0,i∈AS+,≤0,i∈AS0,=0,i=1,...,m

zTH(x∗)z>0,∀x≠0

s.t.h(x)=0g(x)≤0x∈X⊂Rn \begin{aligned} \text{s.t.} &\mathbf{h}(\mathbf{x})=\mathbf{0} \\ &\mathbf{g}(\mathbf{x})\leq \mathbf{0} \\ &\mathbf{x}\in X \subset \mathbb{R}^ n \\  \end{aligned} The impact of the constraints is primarily felt through the feasible region which, as shown in the figures below, can drastically affect the location of the global minimum: As we can see the feasible region can either: change the location of the minimum, leave it unaffected or produce a minimum in an objective function which did not seem to have any. As we can have both equality and inequality constraints, we will consider these individually.

3. [ENTER DESCRIPTION]

dimJi<q

ykfixedk∈Jj

ykfixedk∈Ji

Ji⊂JjJi⊂JjJi\subset Jj)

|NZ|,breakingtheconstraint.The|\mathcal{NZ}|, breaking the constraint. The -1$

|NZ|

n∈0,Un⊂N

(must choose at least one reactor):

P

W(x)=|y1y2 y′1y′2|

route

route

17. Chemical potential of nitrogen along isotherms varying with pressure

E[X|Y=y]=∑xxfX,Y(x,y)

E[X|Y=y]=∫∞−∞xfX,Y(x,y)dx

(not examinable this year)

F(x)=\frac{f(x)}

nA,0−nA(t)−knA(t)vTVR=dnAdt

Interrelations

Gradient

Michaelis-Menton