Table 3 Output of Algorithm A for problem HS8
From: Primal-dual interior point QP-free algorithm for nonlinear constrained optimization
k | \(\boldsymbol{\rho _{k}}\) | \(\boldsymbol{x^{k}}\) | \(\boldsymbol{f(x^{k})}\) | \(\boldsymbol{\Vert \bar{d}^{k} \Vert } \) | \(\boldsymbol{\Vert g^{k}_{\ell } \Vert } \) |
|---|---|---|---|---|---|
0 | 1 | (4, 2) | −1.00000e+00 | 5.09902e+00 | |
1 | 1 | (4.56235, 1.91528) | −1.00000e+00 | 5.70399e−01 | 5.09902e+00 |
2 | 2 | (4.60502, 1.91721) | −1.00000e+00 | 1.02139e−01 | 5.79231e−01 |
3 | 8 | (4.60222, 1.94248) | −1.00000e+00 | 1.07010e−01 | 2.08008e−01 |
4 | 128 | (4.60158, 1.95367) | −1.00000e+00 | 1.83034e−01 | 7.60755e−02 |
5 | 8,192 | (4.60159, 1.95516) | −1.00000e+00 | 1.93245e−01 | 1.32456e−02 |
6 | 8,192 | (4.60159, 1.95575) | −1.00000e+00 | 5.86992e−04 | 4.14795e−03 |
7 | 8,192 | (4.60159, 1.95581) | −1.00000e+00 | 1.24840e−04 | 5.82513e−04 |
8 | 8,192 | (4.60159, 1.95583) | −1.00000e+00 | 2.60839e−05 | 2.36077e−04 |
9 | 8,192 | (4.60159, 1.95584) | −1.00000e+00 | 1.21999e−05 | 7.55776e−05 |