What Are Your Suggestions To These Seemingly Unsolvable Problems?

[xhunt3]

Problems Are:

(1) Let Q = {x € R : Ax = b} and min cTx. Find all points satisfying in the First and Second Order
x£Q
Necessary Conditions.
(2) Let f (x) = cTx. Show that if c ≠ 0, then we can not have an optimal solution lying in interior of Q,
where Q = {x : x € R, Ax = b, x ≥ 0}.
(4) (Steiners problem) In the plane of a given triangle, find a point such that the sum of its distances
from the vertices of the triangle is minimal.
(5) Give an illustrative example for each of the following problems that formulated by a nonlinear
program: Discrete optimal control, Water resources management, Stochastic resource allocation,
Location of facilities, Portfolio optimization and Selection problem.

[RATTER15]

Leave them unsolved.

[Peter Pedant]

4, is clearly computable - Take the sum to be S(x), I would have thought that one could easily construct a path where S(x) is monotone increasing. Ther eis only one point where s(x) is maximum.

5. read the chapter of the set book. Lorentz equations for water sources manaagement. Stochastic resources are exponential so that one should be easy - any one.
Location of facilities - use stockastic processes any is non linear.

1,2 I havent met the relation min cTx so youre on your own on that....

Try reposting in Science

[bert_h]

For 4, it is well-known that the three lines (from the vertices to the required point) must meet at angles of 120 degrees to each other. For any other angles, you can prove that there must be some small displacement which decreases the sum of the distances.