A QP-Free Algorithm for Finite Minimax Problems

Table 1

Numerical results of Algorithm A.

P	IP	n	m	ALG	NI	Approximate solution 𝑥^∗	𝐹(𝑥^∗)	‖𝑑^𝑘‖
1	(1,−0.01)^𝑇	2	3	Algo A	7	(1.1390,0.8995)^𝑇	1.952	1.715𝑒−6
				J2006-1	11	(1.1390,0.8995)^𝑇	1.952	3.462𝑒−7
				J2006-2	19	(1.1390,0.8995)^𝑇	1.952	2.457𝑒−6
				Hu2009	8	—	1.952	4.248𝑒−6
2	(0.01,0.01)^𝑇	2	3	Algo A	7	(1.0000,0.9999)^𝑇	2.000	3.543𝑒−5
				J2006-1	7	(1.0000,1.0000)^𝑇	2.000	6.177𝑒−10
				J2006-2	17	(1.00000,1.00000)^𝑇	2.000	4.775𝑒−9
				Hu2009	7	—	2.000	1.987𝑒−14
3	(0.2,−1,2.3,−0.01)^𝑇	4	4	Algo A	12	(0.0,1.0,2.0,−1.0)^𝑇	−44.00	2.206𝑒−5
				J2006-1	38	(0.0,1.0,2.0,−1.0)^𝑇	−44.00	3.087𝑒−6
				J2006-2	74	(0.0,1.0,2.0,−1.0)^𝑇	−44.00	7.733𝑒−6
				Hu2009	11	—	−44.00	8.294𝑒−6
4	(3,1)^𝑇	2	3	Algo A	11	(−0.45330,0.90659)^𝑇	0.616	9.617𝑒−6
				J2006-1	10	(−0.45329,0.90659)^𝑇	0.616	6.419𝑒−6
				J2006-2	21	(−0.45329,0.90659)^𝑇	0.616	2.641𝑒−6
				Hu2009	12	—	0.616	8.797𝑒−6
5	(1,1,1)^𝑇; (1.01,0.9,1)^𝑇	3	6	Algo A	13	(0.3282,0.0,0.1313)^𝑇	3.599	7.343𝑒−6
				J2006-1	20	(0.3282,0.0,0.1313)^𝑇	3.599	7.227𝑒−7
				J2006-2	34	(0.3282,0.0,0.1313)^𝑇	3.599	3.382𝑒−6
				Hu2009	14	—	3.599	1.832𝑒−6