Optimization problem
Consider the problem: min f(x) s.t. h(x) ? 0 where f (x) = $(x_{1} 1)^2 +2(x_{2}2)^2$ and h(x) = $[1(x_{1})^2 (x_{2})^2,x_{1}+x_{2}]^T$ .
(a) Plot the contour of f(x) and the feasible set on one single figure, i.e., overlay the feasible set on the contour plot of f(x);
(b) Find a solution to the problem using the natural logarithmic barrier function, i.e., the barrier function is $log(h_{1}(x))log(h_{2}(x))$ . Use initialization vector [0.5 0.5]$^{T} $ and the initial penalty parameter equal to 1 and reduce it by $\frac{1}{2} $ in each iteration. Use a stopping threshold of 0.002;
(c) In a 2D figure, plot the trajectory (i.e., the values connected by lines with arrows) of the computed solution vector as the number of iteration progresses.

This sounds like a small optimization project. Your offered bounty is too low. I would also suggest to extend your deadline.

Dont think so, and changing the deadline would mean nothing

Is this a question for numerical analysis? It is not possible to compute the solution analytically, you should use methods like gradient descent algorithm to find the minimizer.

Do you need a code or just the algorithm?

code is preferable

That's too much work! I can write a phsodocode, if you want to implement the code yourself, and graph solutions with a computer on your own.

thats fine just answer every part of the problem

Part c) can not be answered without a code and computing the solutions. So can only answer parts a) and b) and provide a phsodocode.

I suppose thats good enough
Answer
 The questioner was satisfied and accepted the answer, or
 The answer was disputed, but the judge evaluated it as 100% correct.
1 Attachment

For the gradient descent method see: https://en.wikipedia.org/wiki/Gradient_descent
 answered
 226 views
 $30.00
Related Questions
 You have a piece of 8inchwide metal which you are going to make into a gutter by bending up 3 inches on each side
 Evaluate $\int \sin x \sqrt{1+\cos x} dx$
 Determine where the following function is discontinuous
 Compute the surface integral $ \int_S (∇ × F) \cdot dS $ for $F = (x − y, x + y, ze^{xy})$ on the given surface
 Find the arc length of $f(x)=x^{\frac{3}{2}}$ from $x=0$ to $x=1$.
 Maximum gradient of function within a domain
 Basic calc help
 Partial Derivatives and Graphing Functions