第三章单元测试
- In the steepest descent algorithm, any two adjacent search directions are orthogonal to each other
- In the following assertions, which ones are incorrect?
- In a convex programming problem, the equality constraint functions should be linear functions
- Which of the following assertions for the convex function are incorrect?
- Which of the following assertions for the descent direction is incorrect?
A:对 B:错
答案:对
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: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
A:对 B:错
答案:对
A:The Hessian matrix of strictly convex function is positive definite B:If the Hessian matrix of a function is positive semi-definite, then this function is a convex function C:The sum of finitely many convex function is still a convex function D:If any level set of a function is convex then this function is a convex function
答案:The Hessian matrix of strictly convex function is positive definite###If any level set of a function is convex then this function is a convex function
A:For an unconstrained optimization problem,there is no descent direction on the local minimizer of the cost function B:The value of the cost function will decrease along the descent direction C:In an optimization problem, the descent direction might not be a feasible direction. D:When one uses the descent direction to construct a iteration algorithm, the step size should be sufficiently large.
答案:When one uses the descent direction to construct a iteration algorithm, the step size should be sufficiently large.
