An Auxiliary Function Method for Global Minimization in Integer Programming

Table 4

Numerical results of Problem 6 (𝑀=10⁸).

Algorithm	𝑥0	𝑥^∗	𝐸𝑓+𝑔
AFM	[10,−10]^𝑇	[3,0.5]^𝑇	815212
	[0.997,−6.867]^𝑇	[3,0.5]^𝑇	813561
	[0,−1]^𝑇	[3,0.5]^𝑇	414793
	[1,1]^𝑇	[3,0.5]^𝑇	438751
	[−2,2]^𝑇	[3,0.5]^𝑇	537546
	[0,0]^𝑇	[3,0.5]^𝑇	410793
DFMA	[10,−10]^𝑇	[3,0.5]^𝑇	2189978
	[0.997,−6.867]^𝑇	[3,0.5]^𝑇	2192230
	[0,−1]^𝑇	[3,0.5]^𝑇	2197097
	[1,1]^𝑇	[3,0.5]^𝑇	1356906
	[−2,2]^𝑇	[3,0.5]^𝑇	1356906
	[0,0]^𝑇	[3,0.5]^𝑇	2527711
DFMB	[10,−10]^𝑇	[3,0.5]^𝑇	1430248
	[0.997,−6.867]^𝑇	[3,0.5]^𝑇	1431740
	[0,−1]^𝑇	[3,0.5]^𝑇	1439584
	[1,1]^𝑇	[3,0.5]^𝑇	830822
	[−2,2]^𝑇	[3,0.5]^𝑇	829445
	[0,0]^𝑇	[3,0.5]^𝑇	911090