Table 4 HQP algorithm

For iterations 1 to 40

1. Save λ_current →λ_previous

2. Start outer loop to build λ, i = 0 to # elements in M or M_size

 a. w = 0;

 b. start inner loop to build λ, j starts at 0

  i. w = w + P[i][j]∙λ[j]

  ii. GOTO start inner loop If j<M_size,

 c. w = w + K[i]-P[i][i]∙λ[i]

 d. λ_test = -w/P[i][i]

 e. if λ_test < 0 then λ[i] = 0, else λ[i] = λ_test

 f. GOTO start outer loop if i<M_size

3. Check convergence

 a. calculate the Euclidean length of previous λ

 b. calculate the Euclidean length of current λ

 c. Compare ratio to reference value

 d. if converged, exit iteration, GOTO calculate new Δu

4. Else execute next iteration, GOTO 1.

5. Calculate new Δu

 a. Start loop, j = 0 to j=M_size

  i. Δu_c = Δu_c +∙λ[j] ME⁻¹[j]

 b. GOTO start loop if j<M_size

 c. Δu_k+1 = Δu°-Δu_c

6. End