Given the unconstrained function,
F = x₁² + 1/x₁ + x₂ + 1/x₂
F = x₁² + 1/x₁ + x₂ + 1/x₂
Question(a) At x₁ =2 & x₂ = 2, calculate gradient of F.
Question(b) And then, at x₁ =2 & x₂ = 2 , calculate the direction of the deepest descent.
Question(c) Using the direction of the steepest descent from (b), update the design by the standard formula : x¹ = x⁰ + αS¹
Evaluate x₁ , x₂ & F for α=0, 0.2, 0.5, & 1.0 and plot the curve of F versus α.
Question(d) Write the equation for F in terms of α alone. Discuss the character of the function.
Question(e) From (d), calculate dF/dα at α=0.
Question(f) Calculate the scalar product ∇F•S using the results of (a) and (b) and compare this with the result of (e).
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