Exercise · ZW-OPTIMIZATION-PROBLEM-004 · ★☆☆ Basic
What does it mean to minimize a function over a set?
Choose one option.
Show answer
- B. Find the smallest value of the function among the points of the set
Explanation
Minimizing means finding the smallest value of the function within the allowed set. The option that sets the function to zero over the whole space ignores the set.
Review the concept: Optimization problem
An optimization problem consists of minimizing or maximizing an objective function \(f\) over a set of points that satisfy certain constraints.
\[\min_{x \in \mathbb{R}^n} f(x) \quad \text{sujeto a} \quad g_i(x) \le 0\]
More practice problems: optimization problem
- ZW-OPTIMIZATION-PROBLEM-001 What is the general form of an optimization problem with inequality constraints?
- ZW-OPTIMIZATION-PROBLEM-002 What is the name of the function that is minimized in an optimization problem?
- ZW-OPTIMIZATION-PROBLEM-003 What is the name of the set of points that satisfy all the constraints?
- ZW-OPTIMIZATION-PROBLEM-005 What kind of problem is minimizing f(x)=x^2 with no constraints?
- ZW-OPTIMIZATION-PROBLEM-006 Minimize f(x,y)=x^2+y^2 subject to x+y=4. What is the minimum value?
- ZW-OPTIMIZATION-PROBLEM-007 Compute the minimum of f(x)=x^2-4x+7 over all reals.
- ZW-OPTIMIZATION-PROBLEM-008 Maximize f(x,y)=xy subject to x+y=10. What is the maximum value?
- ZW-OPTIMIZATION-PROBLEM-009 Minimize f(x,y)=(x-1)^2+(y-2)^2 subject to x+y≤ 1. What is the optimal point?