Exercise · ZW-OPTIMIZATION-PROBLEM-005 · ★☆☆ Basic
What kind of problem is minimizing \(f(x)=x^2\) with no constraints?
Choose one option.
Show answer
- A. An unconstrained optimization problem
Explanation
There is only an objective function and no constraints, so it is an unconstrained problem. The other options require constraints or structures that do not appear here.
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-004 What does it mean to minimize a function over a set?
- 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?