运筹学（四川师范大学）智慧树知到期末考试答案2024年

运筹学（四川师范大学）智慧树知到期末考试答案2024年运筹学（四川师范大学）The

first

order

necessary

condition

for

a

nonlinear

programming

problem

is

also

a

sufficient

condition

.（

）

A:错误B:正确答案:正确The

convex

function

has

convex

level

sets.（

）

A:正确B:错误答案:正确If

the

basic

feasible

solution

has

zero

components,

then

this

solution

is

degenerate.（

）

A:错误B:正确答案:错For

a

standard

form

LP

problem,

if

a

basic

solution

do

not

have

negative

components,

then

it

is

a

basic

feasible

solution.（

）

A:错B:对答案:对For

an

unconstrained

convex

optimization

problem,

the

iteration

sequence

obtained

by

steepest

descent

method

is

globally

convergent

to

a

minimizer.（

）

A:错误B:正确答案:正确For

an

LP

problem,

if

it

is

bounded,

then

it

has

an

optimal

basic

feasible

solution.（

）

A:正确B:错误答案:错误The

local

minimizer

of

an

LP

problem

is

a

global

minimizer.（

）

A:错误B:正确答案:错The

supremum

of

finitely

many

convex

functions

is

convex.（

）

A:错误B:正确答案:错误If

the

cost

function

is

convex

then

a

local

minimizer

is

also

a

global

minimizer.（

）

A:错误B:正确答案:错If

the

Hessian

matrix

of

a

function

is

positive

semi-definite,

then

this

function

is

convex.（

）

A:正确B:错误答案:正确When

we

describe

the

experiment,

imperative

sentences

are

mostly

used

because

an

important

criterion

for

experiments

is

reproducible,

no

matter

who

does

the

same,

and

therefore

there

is

no

need

to

specify

the

subject.（

）

A:正确B:错误答案:错误In

the

KT

condition,

the

Lagrange

multipliers

for

equality

constraints

should

be

non-negative.（

）

A:正确B:错误答案:错The

relaxed

LP

problem

having

optimal

solutions

implies

the

related

ILP

has

optimal

solutions.（

）

A:正确B:错误答案:错If

the

Hessian

matrix

of

a

function

is

a

null(or

zero)

matrix,

then

this

function

is

convex.（

）

A:正确B:错误答案:正确After

added

the

cutting

plane,

the

feasible

region

of

the

corresponding

ILP

problem

is

strictly

contained

in

the

original

ILP

problem.（

）

A:错误B:正确答案:正确For

a

standard

form

LP

problem,

if

a

basic

solution

do

not

have

negative

components,

then

it

is

a

basic

feasible

solution.（

）

A:错B:对答案:AI参考:答案：B。根据线性规划问题的标准形式，如果基本解中没有负数，那么它就是一个基本可行解。所以这个题目的判断题是正确的。'The

solution

to

the

LP

problem

is

（

）.

A:

B:C:D:

答案:AI参考:答案选D，ThesolutiontotheLPproblemis…is后面接名词或动名词作同位语，所以选项D正确。'Which

of

the

following

part

in

a

paper

is

the

most

difficult

and

time-consuming

to

read

?

（

）

A:Introduction.B:Method

and

result.C:Analyses

and

discussion.D:Figures

and

tables.答案:AI参考:正确答案是B:Method

and

result。\n\n阅读一篇论文时，通常需要花费最多时间和精力的部分是方法（Method）和结果（Result），因为这部分通常涉及到实验过程和数据结果的分析，需要仔细阅读和理解。而引言（Introduction）、分析（Analyses）和讨论（Discussion）、图表（Figures

and

tables）等部分相对来说比较容易理解和阅读。因此，选项B是正确答案。'The

residual

variable

is

（

）

A:introduced

to

replace

a

free

variable.B:an

artificial

variable

introduced

in

the

auxiliary

problem.C:introduced

to

transform

a

greater-than-or-equal-to

inequality

constraint

into

the

equality

constraint.D:introduced

to

transform

a

less-than-or-

equal-to

inequality

constraint

into

the

equality

constraint.答案:AI参考:正确答案是【D:introduced

to

transform

a

less-than-or-equal-to

inequality

constraint

into

the

equality

constraint.】。\n\n在给定的句子中，“剩余变量”是被引入以将小于或等于的不等式约束转化为等式约束，所以正确选项为D，即将小于或等于的不等式约束转化为等式约束。其他选项A、B、C都与句子中的描述不符。'In

the

following

assertions

for

the

basis

matrix

of

an

LP

problem

with

standard

form,

which

one

is

incorrect（

）

A:The

feasible

basis

matrix

might

not

exist.B:The

basis

matrix

is

uniquely

determined

for

a

given

basic

solution.C:The

column

vectors

of

a

basis

are

linearly

independent.D:The

number

of

basis

matrix

is

finite.答案:AI参考:正确答案是A:The

feasible

basis

matrix

might

not

exist.。\n\n对于一个标准形式的线性规划问题的基矩阵，存在可行基矩阵，因此选项B和C都是正确的。基矩阵的列向量是线性独立的，因此选项C也是正确的。可行基矩阵的数量是有限的，因此选项D也是正确的。因此，只有选项A是错误的，即可行基矩阵可能不存在。'The

dual

linear

programming

problem

of

the

linear

programming

problem

is

（

）

.

A:B:C:D:答案:AI参考:正确答案是D:线性规划问题与对偶问题的关系中，对偶线性规划问题就是原线性规划问题的最优解所对应的原问题的最优解所对应的原问题的最优解。\n\n所以答案是D。\n\n注意：此题为单选题，所以答案只有一个。其他选项都是干扰项。'If

x

is

a

basic

feasible

solution

of

a

standard

form

LP

problem,

then（

）

A:its

nonbasic

variables

are

zeroes.B:it

has

only

one

basis.C:its

basic

variables

are

positive.D:the

number

of

its

positive

components

is

less

than

the

number

of

rows

of

the

constraint

matrix.答案:AI参考:正确答案是D:the

number

of

its

positive

components

is

less

than

the

number

of

rows

of

the

constraint

matrix.\n\n如果x是一个标准形式LP问题的基本可行解，那么它的正系数之和小于约束矩阵的行数。选项A和B与问题描述不符，选项C不正确，因为基本变量可以是零或正数。因此，答案为D。'The

special

solution

to

the

canonical

equation

that

the

nonbasic

variables

are

equal

to

zeros

is

a

（

）

A:feasible

solution.B:basic

solution.C:standard

solution.D:regular

solution.答案:AI参考:正确答案是A:feasible

solution。\n题干中提到非基本变量等于零的特殊解，这个解是可行的，因此答案为A。B选项“基本解”和C选项“标准解”与题意不符，D选项“正规解”虽然与题意有关，但不是正确答案。因此，答案为A。'The

regular

solution

of

an

LP

problem

is

（

）

A:non-negativeB:dual

feasibleC:degenerateD:a

vertex

of

the

feasible

region答案:AI参考:正确答案是D:avertexofthefeasibleregion。\n本题考查线性规划问题的解的概念，选项A表示非负解，选项B表示对偶可行解，选项C表示退化解，而选项D表示可行域的顶点，即线性规划问题的最优解。因此，答案为D。'Which

one

of

the

follow

cases

might

happen?（

）

A:The

optimal

values

of

the

primal

LP

problem

and

dual

LP

problem

are

equal.B:The

optimal

value

of

the

primal

LP

problem

is

strictly

larger

than

the

one

of

dual

LP

problem.C:The

optimal

value

of

the

primal

LP

problem

is

strictly

less

than

the

one

of

dual

LP

problem

.D:The

optimal

values

of

both

the

primal

LP

problem

and

the

dual

LP

problem

are

infinite.答案:AI参考:正确答案是B:TheoptimalvalueoftheprimalLPproblemisstrictlylargerthantheoneofdualLPproblem.。\n\n根据线性规划的基本理论，当原问题与对偶问题同时最优时，最优解的值相等；当原问题最优解的值大于对偶问题的最优解时，原问题最优；当原问题最优解的值小于对偶问题的最优解时，原问题次优。因此，选项B正确，即原问题最优解的值大于对偶问题的最优解，即情况可能会发生。其他选项都与线性规划理论不符。'

A:Both

the

globally

optimal

solution

and

the

locally

optimal

solution

satisfy

the

first

order

necessary

optimality

condition

.B:The

globally

optimal

solution

is

also

a

locally

optimal

solution.C:The

locally

optimal

solution

is

also

a

globally

optimal

solution.D:For

a

convex

programming

problem,

a

locally

optimal

solution

coincides

with

a

globally

optimal

solution.答案:AI参考:正确选项是D：对于一个凸规划问题，一个局部最优解与全局最优解相一致。\n\n根据题目中的描述，选项A表示全球最优解和局部最优解都满足一阶最优性条件，但没有明确说明两者之间的关系。选项B和C则分别表示全球最优解是局部最优解，或者局部最优解是全球最优解，但都没有直接回答问题。只有选项D明确指出对于一个凸规划问题，局部最优解与全局最优解是一致的。因此，选项D是正确的答案。'In

the

simplex

tableau

for

two-phase

method

we

have

that

(

)

A:the

optimal

solution

to

the

auxiliary

problem

is

(0,9/4,

7/4,0,3/4,0

)T.B:the

solution

to

the

original

problem

is

(0,9/4,

7/4

)T.C:the

feasible

region

of

the

original

problem

is

an

empty

set.D:it

should

be

iterated

again

since

the

artificial

variable

x5

is

basic

variable.答案:AI参考:正确选项是【B:thesolutiontotheoriginalproblemis(0,9/4,

7/4

)T.】。\n\n根据图中的简单表图，原始问题的解为(0,9/4,7/4)T，而辅助问题的最优解为(0,9/4,7/4,0,3/4,0)T，因此选项B是正确的。选项A、C、D与图中的信息不符。选项D指出应该再次迭代，因为人工变量x5是基本变量，但这并不适用于此问题。'If

the

feasible

region

of

a

LP

problem

is

nonempty,

then

（

）

A:the

LP

problem

is

bounded.B:the

feasible

region

is

convex.C:the

LP

problem

has

basic

feasible

solution.D:the

LP

problem

has

optimal

solution.答案:AI参考:正确选项为：D:the

LP

problem

has

optimal

solution.\n\n如果一个线性规划问题的可行域非空，那么该线性规划问题存在最优解。其他选项A、B、C不一定成立。具体来说，选项A没有直接与可行域非空有关；选项B可行域不一定是凸的；选项C的基本可行解不一定是最优解。'From

the

simplex

tableau

（for

an

ILP

problem）we

can

introduce

(

)

as

the

cutting

planes.

A:.B:

.C:.D:

.答案:AI参考:正确选项是D：A\n\n根据多选题要求，需要从给出的选项中选择两个或两个以上的正确答案。从题目给出的图片中可以看出，这是一个ILP（整数线性规划）问题的简单表图。根据表图的结构和内容，我们可以引入割平面（cuttingplanes）来解决该问题。割平面是一种解决整数线性规划问题的方法，通过在约束条件中引入一些额外的变量，将问题转化为一系列子问题，最终得到最优解。因此，选项D是正确的答案。选项A和B描述的是割平面的引入方式，而选项C描述的是割平面的作用，与题目要求不符。'In

the

following

assertions

for

the

feasible

region

of

ILP

problem,

which

ones

are

correct（

）

A:The

feasible

region

is

nonconvex

when

it

has

more

than

one

feasible

solutions.B:The

feasible

region

h