- #1

sdevoe

- 21

- 0

## Homework Statement

Consider the following optimization problem:

min f(x)

s.t. g(x) ≥ 0

h(x) ≤ 0

q(x) = 0

Let xbar satisfy g(x) = h(x) = q(x) = 0.

a)State and prove a set of necessary and sufficient conditions for x to be a local minimum.

b)How would the conditions change if g(x) = q(x) = 0; h(x) < 0? You do not have to

present the proof for this case. Just write down the new set of conditions.

## Homework Equations

NONE

## The Attempt at a Solution

I am completely stumped on this one. Besides the obvious x must lie within the region. Is there something to do with the region only being one point and not an actual region