运筹学（四川师范大学）章节测试课后答案2024春

第三章测试

1.Which of the following assertions for the descent direction is incorrect?
A:For an unconstrained optimization problem,there is no descent direction on the local minimizer of the cost function B:When one uses the descent direction to construct a iteration algorithm, the step size should be sufficiently large. C:The value of the cost function will decrease along the descent direction D:In an optimization problem, the descent direction might not be a feasible direction.
答案:B
2.Which of the following assertions for the convex function are incorrect?
A:If the Hessian matrix of a function is positive semi-definite, then this function is a convex function B:The Hessian matrix of strictly convex function is positive definite C:If any level set of a function is convex then this function is a convex function D:The sum of finitely many convex function is still a convex function
答案:BC
3.In a convex programming problem, the equality constraint functions should be linear functions
A:错 B:对
答案:B
4.In the following assertions, which ones are incorrect?
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:In an unconstrained optimization problem, the stationary points of the convex cost function are global minimizers C:If the inner product of a vector p and the gradient vector is negative, then p is a descent direction D:To solve a constrained convex programming problem, we only need to find the KKT points of this convex programming problem
答案:A
5.In the steepest descent algorithm, any two adjacent search directions are orthogonal to each other
A:对 B:错
答案:A