On the Solution of a Nonlinear Semidefinite Program Arising in Discrete-Time Feedback Control Design

Table 2

Convergence behavior of the methods NM and DSQP for Example 17.

𝑘	𝐽𝑘̂	‖∇𝐽𝑘̂‖	𝑘	𝐽𝑘	‖∇𝑈ℓ𝑘‖	𝑡𝑘
1	2.7105𝑒+003	1.3120𝑒+005	1	1.9178𝑒+003	5.4776𝑒+004	2.00𝑒−003
2	4.0079𝑒+003	2.2196𝑒+005	2	1.9541𝑒+003	3.9033𝑒+004	1.60𝑒−003
3	6.0553𝑒+003	3.4516𝑒+005	3	2.4908𝑒+003	3.4364𝑒+004	1.02𝑒−003
⋮	⋮	⋮	⋮	⋮	⋮	⋮
19	1.5413𝑒+003	2.3402𝑒−001	16	1.5413𝑒+003	1.9083𝑒−002	1.32𝑒−016
20	1.5413𝑒+003	4.6373𝑒−003	17	1.5413𝑒+003	2.2029𝑒−006	2.98𝑒−018
21	1.5413𝑒+003	7.4319𝑒−007	18	1.5413𝑒+003	3.8485𝑒−011	5.36𝑒−020