Free Printable Optimization Techniques Unit-2- QUIZ

1.

What represents 1, 2 and 3 in sequence ?

a)

Minima, Maxima and Inflection

b)

Minima, Inflection and Maxima

c)

Maxima, Inflection and Minima

d)

Inflection, Minima and Maxima

2.

Local (or) Relative Minima

a)

f(x^*) ≥ f(x^* + h)

b)

f(x^*) ≤ f(x^* + h)

c)

f(x^*) ≥ f(x)

d)

f(x^*) ≤ f(x)

3.

Identify correct options

a)

Local Maxima - B, C

b)

Local Maxima - A, B, C

c)

Local Maxima - P, Q

d)

Local Minima - P, Q

e)

Global Maxima - C

4.

In Working Rule (Algorithm) for Unconstrained Multivariable optimization equations of J1 and J2

a)

$J_1=|(∂^2f)/(∂x_1^2)|$

b)

$J_1=|(∂^2f)/(∂x_2^2)|$

c)

d)

5.

Most important Solution Methods for Multivariable Optimization with Equality constraints are

a)

Direct Substitution Method

b)

Gauss-Jordan method

c)

Constrained Variation Method

d)

Lagrange Multipliers Method

e)

Cramer’s rule

6.

Lagrange Multipliers Method suitable only when

m - No. of Constraints

n - No. of Variables

a)

$m>n$

b)

$m=n$

c)

$m<n$

7.

Kuhn-Tucker Conditions are

a)

b)

$λ_j〖g〗_j=0,\ \ \ \ \ \ \ j=1,2,…,m$

c)

$〖g〗_j≤0,\ \ \ \ \ \ \ \ j=1,2,…,m$

d)

$〖λ〗_j≥0,\ \ \ \ \ \ j=1,2,…,m$

8.

The Lagrange Function can be written as

a)

$L(x,λ)=f(x_1,x_2)+λg_1(x_1,x_2)+λg_2(x_1,x_2)$

b)

$L(x,λ)=f(x_1,x_2)+λ_1g_1(x_1,x_2)+λ_2g_2(x_1,x_2)$

c)

$L(x,λ)=f(x_1,x_2)+λ_1g(x_1,x_2)+λ_2g(x_1,x_2)$

9.

Lagrange Function

a)

$L(x_i,λ_j)=f(x_i)+λ〖g〗(x_i)$

b)

$L(x_i,λ_j)=f(x)+λ_j〖g〗(x_i)$

c)

$L(x_i,λ_j)=f(x)+λ〖g〗_j(x_i)$

d)

$L(x_i,λ_j)=f(x_i)+λ_j〖g〗_j(x_i)$

10.

Kuhn and Tucker are

a)

Scientists

b)

Mathematicians

c)

Physicians

Optimization Techniques Unit-2- QUIZ - 17-04-2020

Total questions: 10

Worksheet time: 10mins

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