Section A: (70 points) Develop your own Matlab/Phyton code for a line search based on Golden...

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Section A: (70 points) Develop your own Matlab/Phyton code for a line search based on Golden Section Search Method which is to be utilized in determination of the optimum step size a* of change in design A. We will use this code in the next nonlinear programming textbook. assignment. Verify your code with the solved exercises in your Section B: (30 points) For the following two functions, direction of change at a point is given. a) f(x)=(a*x +3* x +d* x) +4*h* (x - x) = (1,3,1) at =(-1,-1,-1) at x = (5,1) d = (-1,-2) b) f(x)=0.1*a* x +d* x -10 Where you will use your university student id number to determine a,b,c,d,e,f,g,h,i. Your number is [abcdefghi]. If you need to make any minor adjustment to your problems because of your ID number, please explain why and proceed with it. For each problem, 1) Derive the function of one variable (line search function) that can be used to determine the optimum step size. Show your steps. (7.5 points each) 2) Then, using your Golden Section search Matlab Phyton code, calculate the optimum step size a with = 0.05 and = 0.0001 at the given point and the search direction. (7.5 points each) Please submit a) Soft copy of your Matlab program (no bugs) Your code must run without errors. b) A technical paper of your work (clear, fluent, complete, understandable, must have formulations, flowchart and a good discussion). Please use AIAA class template for your report. Technical report is mandatory. c) Submit your homework to Ninova on time. No emails will be accepted. Section A: (70 points) Develop your own Matlab/Phyton code for a line search based on Golden Section Search Method which is to be utilized in determination of the optimum step size a* of change in design A. We will use this code in the next nonlinear programming textbook. assignment. Verify your code with the solved exercises in your Section B: (30 points) For the following two functions, direction of change at a point is given. a) f(x)=(a*x +3* x +d* x) +4*h* (x - x) = (1,3,1) at =(-1,-1,-1) at x = (5,1) d = (-1,-2) b) f(x)=0.1*a* x +d* x -10 Where you will use your university student id number to determine a,b,c,d,e,f,g,h,i. Your number is [abcdefghi]. If you need to make any minor adjustment to your problems because of your ID number, please explain why and proceed with it. For each problem, 1) Derive the function of one variable (line search function) that can be used to determine the optimum step size. Show your steps. (7.5 points each) 2) Then, using your Golden Section search Matlab Phyton code, calculate the optimum step size a with = 0.05 and = 0.0001 at the given point and the search direction. (7.5 points each) Please submit a) Soft copy of your Matlab program (no bugs) Your code must run without errors. b) A technical paper of your work (clear, fluent, complete, understandable, must have formulations, flowchart and a good discussion). Please use AIAA class template for your report. Technical report is mandatory. c) Submit your homework to Ninova on time. No emails will be accepted.