第一章 单元测试
1、判断题：
A basic feasible solution of an LP problem have one and only one related feasible basis.
选项：
A:对
B:错
答案: 【错】
2、判断题：
If the primal LP problem is unbounded, then the feasible region of dual problem must be empty.
选项：
A:对
B:错
答案: 【对】
3、多选题：
If the LP problem is solvable, then
选项：
A:The feasible region of this LP problem is nonempty
B:There exists an optimal basic feasible solution to this LP problem
C:There is a feasible regular solution of this LP problem
D:The value of the LP problem is finite
答案: 【The feasible region of this LP problem is nonempty;There exists an optimal basic feasible solution to this LP problem;There is a feasible regular solution of this LP problem;The value of the LP problem is finite】
4、多选题：
If the primal LP problem has optimal solutions, then
选项：
A:The dual problem is bounded
B:The feasible region of the dual problem is nonempty
C:The dual problem is non-degenerate
D:The dual problem has an optimal basic feasible solution
答案: 【The dual problem is bounded;The feasible region of the dual problem is nonempty;The dual problem has an optimal basic feasible solution】
5、单选题：
Which of the following assertions for the feasible region of a standard LP problem is incorrect?
选项：
A:The feasible region might have infinitely many vertices
B:The feasible region is convex
C:The feasible region might not have vertex
D:The feasible region might be unbounded
答案: 【The feasible region might have infinitely many vertices】
第二章 单元测试
1、判断题：
If the relaxed LP problem has feasible solution, then the related ILP problem has nonempty feasible region
选项：
A:对
B:错
答案: 【错】
2、判断题：
After adding the cutting plane, the new simplex table corresponds to a regular solution to the new LP problem
选项：
A:对
B:错
答案: 【对】
3、判断题：
In the branch-and-bound method, the bound is the value of cost function on a integer optimal solution to some relaxed sub-problem
选项：
A:对
B:错
答案: 【对】
4、多选题：
Which of the following assertions for the branch-and-bound method are correct?
选项：
A:If the value of current sub-problem is larger than the bound, the branch for this sub-problem should be cut off.
B:If the current sub-problem has integer optimal solution and the value is smaller than the bound, then the integer optimal solution is the solution to the original problem.
C:If the value of the sub-problem is smaller than the current bound and the optimal solution is not an integer solution, then this branch should be cut off.
D:If the corresponding relaxed LP problem has an integer optimal solution, then this solution is the optimal solution of ILP problem
答案: 【If the value of current sub-problem is larger than the bound, the branch for this sub-problem should be cut off.;If the corresponding relaxed LP problem has an integer optimal solution, then this solution is the optimal solution of ILP problem】
5、多选题：
Which of the following assertions for the cutting plane method are correct?
选项：
A:After adding the cutting plane, if the new relaxed problem is unsolvable then, the original ILP is unsolvable
B:In the procedure of solving ILP by cutting plane method,the feasible region of the relaxed LP problem will become smaller in each iteration.
C:After adding the cutting plane,one should using the dual simplex method to solve the new relaxed problem
D:If the relaxed problem has feasible solution, then the ILP problem has feasible solution
答案: 【After adding the cutting plane, if the new relaxed problem is unsolvable then, the original ILP is unsolvable;In the procedure of solving ILP by cutting plane method,the feasible region of the relaxed LP problem will become smaller in each iteration.;After adding the cutting plane,one should using the dual simplex method to solve the new relaxed problem】
第三章 单元测试
1、单选题：
Which of the following assertions for the descent direction is incorrect?
选项：
A:The value of the cost function will decrease along the descent direction
B:In an optimization problem, the descent direction might not be a feasible direction.
C:When one uses the descent direction to construct a iteration algorithm, the step size should be sufficiently large.
D:For an unconstrained optimization problem,there is no descent direction on the local minimizer of the cost function
答案: 【When one uses the descent direction to construct a iteration algorithm, the step size should be sufficiently large.】
2、多选题：
Which of the following assertions for the convex function are incorrect?
选项：
A:The sum of finitely many convex function is still a convex function
B:If any level set of a function is convex then this function is a convex function
C:The Hessian matrix of strictly convex function is positive definite
D:If the Hessian matrix of a function is positive semi-definite, then this function is a convex function
答案: 【If any level set of a function is convex then this function is a convex function;The Hessian matrix of strictly convex function is positive definite】
3、判断题：
In a convex programming problem, the equality constraint functions should be linear functions
选项：
A:对
B:错
答案: 【对】
4、单选题：
In the following assertions, which ones are incorrect?
选项：
A:In an unconstrained optimization problem,if the Hessian matrix on a stationary point of the cost function is positive semi-definite then, the stationary point is a local minimizer
B:To solve a constrained convex programming problem, we only need to find the KKT points of this convex programming problem
C:In an unconstrained optimization problem, the stationary points of the convex cost function are global minimizers
D:If the inner product of a vector p and the gradient vector is negative, then p is a descent direction
答案: 【In an unconstrained optimization problem,if the Hessian matrix on a stationary point of the cost function is positive semi-definite then, the stationary point is a local minimizer】
5、判断题：
In the steepest descent algorithm, any two adjacent search directions are orthogonal to each other
选项：
A:错
B:对
答案: 【对】
第四章 单元测试
1、多选题：
When we write scientific papers, what kind of words are often used ?
选项：
A:compound words
B:antonyms
C:acronyms
D:oral words
答案: 【compound words;antonyms;acronyms】
2、单选题：
If some results has been found in the past and they still have an impact on the present, what kind of tense we need to use in the writing ?
选项：
A:past tense
B:present perfect tense
C:future tense
D:present tense
答案: 【present perfect tense】
3、判断题：
We need to read carefully the entire content for any paper.
选项：
A:错
B:对
答案: 【错】
4、判断题：
Basic function of author’s name is only to raise author’s prestige.
选项：
A:对
B:错
答案: 【错】
5、多选题：
In the following strategies, which can help us improve reading efficiency?
选项：
A:Only read introduction part
B:Focus your time on literature reading
C:Use translation software to translate the full text
D:read in an order
答案: 【Focus your time on literature reading;read in an order】
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