For years, private equity giants have worked to change a damaging public perception in Japan: that they’re "vultures,” hacking companies apart and gorging on their remains.

Now, Toshiba is giving the buyout industry an $18 billion opportunity to see whether those efforts have paid off.

The troubled Japanese conglomerate is soliciting acquisition offers — and other proposals — as it seeks to end years of mismanagement. Bain Capital, Blackstone Inc. and CVC Capital Partners are among the funds considering bids. A successful deal, which may be private equity’s largest ever in the country, would signal the once-criticized investors have become more accepted in Japan.