Which of the following statements is false about convex minimizat
| Which of the following statements is false about convex minimization problem?
A. If a local minimum exists, then it is a global minimum
B. The set of all global minima is convex set
C. The set of all global minima is concave set
D. For each strictly convex function, if the function has a minimum, then the minimum is unique
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
A convex optimization problem is one of the form:
Minimize f0(x)
Subject to fi(x)<=bi where i = 1,……..m
Where the functions f0,……….fm : Rn -> R are convex i.e.
Satisfy fi (ax + by) <= afi(x) + bfi(y)
A convex optimization problem is a problem where all of the constraints are convex functions and objective is a convex function if it is minimizing. If function is maximizing, then it is concave function.
Some points about convex problems are:
- With a convex objective and convex feasible region, there can be only one optimal solution which is globally optimal.
- Convex problem can be solved efficiently up to large size
- There are two methods to solve convex problems: interior point or barrier methods.
- Every local minimum exists in the problem is also a global minimum.
- Set of all global minima is a convex set.
- Set of all global maxima is a concave set
- For each strictly convex function, if the function has a minimum, then the minimum is unique .