story identification - Book: industrialist with private island hires woman computer expert to talk to his self-aware computer

I’m currently trying to find the name of a book that wasn’t very old that I read about 10 years ago. It had a super genius industrialist, who reminded me of Bill Gates, who hired a woman computer expert to come and investigate his supercomputer which was becoming self-aware. His large company and home were on an island and he had his own rocket port. He was going to harvest asteroids and the government sent the military to try to stop him.

Answer

Your question reminds me of this old question. The answer to that one was Society of the Mind by Eric L. Harry. A review at Google Books:

Society of the Mind is the story of Dr. Laura Aldridge, a young Harvard psychology professor who is offered a seven-figure sum for a week of unspecified consultation by enigmatic inventor and computer genius Joseph Gray. Unknown to all but Gray's immediate staff, his prized invention and alter-ego - a massive, artificially intelligent neurocomputer - lies buried deep underground; its "mind" has grown troubled and its wide-ranging errors cause for grave concern. When Laura meets Gray on his south Pacific island, she is shocked - but intrigued - when she learns exactly what her job entails: to psychoanalyze and "cure" Gray's aberrant mainframe, which has become all too human in its operation, before its malfunctions lead to global catastrophe. But what Gray has built is not only a thinking entity; it feels as well. A conscious, brilliant, neurotic, and lonely mind that looks out at the world through cameras, interacting with it by way of the faltering steps of inquisitive, childlike robots, the neurocomputer shares its world with Laura when she immerses herself in Gray's virtual-reality workstations. And the closer Laura gets to the crux of the neurocomputer's psychological problems, the more engaging and "talkative" it becomes - until it begins to have trouble keeping its inventor's potentially devastating secrets. Utterly riveting, Society of the Mind raises questions that are chillingly real: As computer scientists succeed in replicating the human mind, what happens when they mistakenly - or perhaps intentionally - replicate its psychotic tendencies as well? And if the virus of human madness can be caught by computers, can the contagion pass from computers back to man?