第三章测试
1.Which of the following assertions for the descent direction is incorrect?
A:In an optimization problem, the descent direction might not be a feasible direction. B:The value of the cost function will decrease along the descent direction C:For an unconstrained optimization problem,there is no descent direction on the local minimizer of the cost function D:When one uses the descent direction to construct a iteration algorithm, the step size should be sufficiently large.
答案:D
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: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: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:对 B:错
答案:A
4.In the following assertions, which ones are incorrect?
A:If the inner product of a vector p and the gradient vector is negative, then p is a descent direction B:In an unconstrained optimization problem, the stationary points of the convex cost function are global minimizers C:To solve a constrained convex programming problem, we only need to find the KKT points of this convex programming problem D: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
答案:D
5.In the steepest descent algorithm, any two adjacent search directions are orthogonal to each other
A:对 B:错
答案:A

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