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Faculty Assignment2 Q2 · Specified momentum update

Faculty Assignment 2 · worked practice

Question

Question. For J(w)=½(w+2)²,η=0.2,β=0.8,w₀=4,v₀=0,perform one momentum step. (Faculty assignment: no marks printed)

Answer — step by step

Given

All givens above.

To find

v₁andw₁.

Formula: which one and why

g=w+2,\quad v_1=\beta v_0+\eta g,\quad w_1=w_0-v_1LaTeX: g=w+2,\quad v_1=\beta v_0+\eta g,\quad w_1=w_0-v_1

Step 1. Gradient

g₀=4+2=6.

Step 2. Momentum displacement

v₁=0.8×0+0.2×6=1.2.

Step 3. Weight

w₁=4−1.2=2.8.

Final answer

v₁=1.2,w₁=2.8. A signed-velocity convention givesv₁=−1.2andw₁=w₀+v₁; the final weight is the same.