(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

NONE

3. 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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Necessary conditions for a linear program

**Physics Forums | Science Articles, Homework Help, Discussion**