Problem 1 Consider the following 2D function: f(x, x) = x + xx + 2x +5...

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Problem 1 Consider the following 2D function: f(x₁, x₂) = x² + x₁x₂ + 2x² +5 Suppose an iterative method manages to optimize this function with two steps, starting with an initial design at xº = (3,2). In the first step, the search direction is dº= (-1,-1) and the step size is aº = 1.0. In the second step, the search direction is d¹ = (-1,-0.5) and the step size is a¹ = 2.0. a) Calculate the design variable and objective function values for each step, i.e., xº, x¹, and x² and f(xº), f(x¹), and f(x²). (40%) b) Use MATLAB to plot the contour of this function and add labels to the contour lines. Then, plot the locations of x0, x¹, and x² as symbols and connect them with solid lines to show the trajectory of optimization process. Finally, use the text command to annotate the locations for xº, x¹, and x2 in the plot. Attach the plot to the solutions and upload the MATLAB code to Canvas. (60%) Problem 1 Consider the following 2D function: f(x₁, x₂) = x² + x₁x₂ + 2x² +5 Suppose an iterative method manages to optimize this function with two steps, starting with an initial design at xº = (3,2). In the first step, the search direction is dº= (-1,-1) and the step size is aº = 1.0. In the second step, the search direction is d¹ = (-1,-0.5) and the step size is a¹ = 2.0. a) Calculate the design variable and objective function values for each step, i.e., xº, x¹, and x² and f(xº), f(x¹), and f(x²). (40%) b) Use MATLAB to plot the contour of this function and add labels to the contour lines. Then, plot the locations of x0, x¹, and x² as symbols and connect them with solid lines to show the trajectory of optimization process. Finally, use the text command to annotate the locations for xº, x¹, and x2 in the plot. Attach the plot to the solutions and upload the MATLAB code to Canvas. (60%)

Answer rating: 100% (QA)

a To calculate the design variable and objective function values for each step we can use the follow... View the full answer