Gradient and steepest descent methods

Reference no: EM13924368

Gradient and steepest descent methods

1. Quadratic problem in R². Verify the expressions for the iterates x^(k).

2. Let Δx_sd and Δx_sdbe the normalized and unnormalized steepest descent directions at x, for the norm ||.||. Prove the following identities.

(a) ∇ f(x)^TΔx_nsd = -||∇f(x)||_*.

(b) ∇ f(x)^TΔx_sd = -||∇f(x)||²_*.

3. Steepest descent method in l_∞-norm. Explain how to find a steepest descent direction in the l_∞-norm, and give a simple interpretation.

Reference no: EM13924368

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