Exercise · ZW-WOLFE-CONDITIONS-004 · ★☆☆ Basic
If a step \(\alpha\) satisfies both Wolfe conditions, what is guaranteed?
Choose one option.
Show answer
- B. Sufficient decrease and that the step is not too short
Explanation
Satisfying both conditions guarantees sufficient decrease and that the slope has increased enough. It does not guarantee global optimality.
Review the concept: Wolfe conditions
Two inequalities that a line-search step \(\alpha\) must satisfy to guarantee sufficient decrease of the function and that the step is not too short.
\[f(x_k+\alpha p_k)\le f(x_k)+c_1\alpha\nabla f(x_k)^\top p_k\]
More practice problems: wolfe conditions
- ZW-WOLFE-CONDITIONS-001 Which condition requires the function to decrease enough relative to its initial value?
- ZW-WOLFE-CONDITIONS-002 Which Wolfe condition prevents the step from being too short?
- ZW-WOLFE-CONDITIONS-003 In the Wolfe conditions, what relation must the constants c_1 and c_2 satisfy?
- ZW-WOLFE-CONDITIONS-005 What is the name of the variant that bounds the slope at the new point in absolute value?
- ZW-WOLFE-CONDITIONS-006 Let f(x)=x^2, x_k=1, p_k=-1, c_1=0.1. Does α=0.5 satisfy the Armijo condition?
- ZW-WOLFE-CONDITIONS-007 Let f(x)=x^2, x_k=1, p_k=-1, c_1=0.1, c_2=0.9. Which condition fails with α=2?
- ZW-WOLFE-CONDITIONS-008 A step α that is too short barely changes the gradient. Which Wolfe condition rejects it?
- ZW-WOLFE-CONDITIONS-009 Let f(x)=x^2, x_k=1, p_k=-1, c_1=0.1, c_2=0.9. What happens with α=0.01?