please use matlab and explain code and outputs.

We consider to minimize the function f(x)=x + , with either one or both of the equality constraint (01 - 2)2 + x3 - 1 = 0 and the inequality constraint 11 +22-22 0. 1. Consider to solve the equality constrained optimization problem min x + x3 subject to (01 - 2)2 + 23 - 1 = 0. (a) Write out the KKT conditions for the solution of this problem. Solve for x satisfying the KKT conditions and determine if it is a solution of this constrained minimization problem. (b) Apply the Quadratic Penalty method discussed in the lecture to solve this optimization problem with equality constraint. In the Quadratic Penalty algorithm, you can take Ho = 1.0 and To = 1.0 x 10-5, and take the initial point x = (4,2). In each step of the Quadratic Penalty algorithm, you can take the+1 = m/2 and Tk+1 = 1./2. The convergence is achieved when i