Gradient descent optimizer should find optimal coefficient values

Formula, using for gradient descent:

c_i = c_i-1 - η * g

where:

• i - number of iteration
• c - vector of coefficients
• η - leraning rate
• g - gradient vector

iteration 1:

Precalculated gradient vector, g, - (8, 8, 8)

Previously calculated coefficient vector, c^’, - (0, 0, 0)

Learning rate, η, - 2.0

c₁ = c₁^’ - η * g₁ = 0 - 2 * 8 = -16

c₂ = c₂^’ - η * g₂ = 0 - 2 * 8 = -16

c₃ = c₃^’ - η * g₃ = 0 - 2 * 8 = -16

c = (-16, -16, -16)

iteration 2:

Precalculated gradient vector, g, - (8, 8, 8)

Previously calculated coefficient vector, c^’, - (-16, -16, -16)

Learning rate, η, - 2.0

c₁ = c₁^’ - η * g₁ = -16 - 2 * 8 = -32

c₂ = c₂^’ - η * g₂ = -16 - 2 * 8 = -32

c₃ = c₃^’ - η * g₃ = -16 - 2 * 8 = -32

c = (-32, -32, -32)

iteration 3:

Precalculated gradient vector, g, - (8, 8, 8)

Previously calculated coefficient vector, c^’, - (-32, -32, -32)

Learning rate, η, - 2.0

c₁ = c₁^’ - η * g₁ = -32 - 2 * 8 = -48

c₂ = c₂^’ - η * g₂ = -32 - 2 * 8 = -48

c₃ = c₃^’ - η * g₃ = -32 - 2 * 8 = -48

c = (-48, -48, -48)