Sudden restarts while using bootable USB installer (mid-2011 iMac) - evidence of hardware problem?

Question

Greetings:
For a couple of years I've been suffering from an issue reported in many threads:  seemingly random shutdowns and restarts of my mid-2011 iMac.  These can happen several times a day, or there can be a gap of weeks between occurences.  I've searched the web and discussions.apple.com endlessly, and tried every conceivable solution.  I've observed no consistent pre-restart pattern in Console.  I've tried removing all unnecessary extensions and start-up programs.  Fixed permissions, repaired HDD, many of the diagnostic procedures described by LINC (superuser on this forum).  I would sometimes get temporary relief from periodic restart loops, by unplugging the computer and resetting PRAM, but this would not last long. I couldn't discern whether it is a software/conflict issue, or a hardware issue.  Have run AHT in extended looping mode, several times, and found nothing wrong.  Which caused me to keep thinking it must be a software issue.  The last thing I've tried is a clean install of Yosemite, with full HDD erase, from bootable USB.
I did this successfully, restored files from Time Machine...but then a few hours later, a series of sudden restarts began, with 4 or 5 within a couple of hours. I decided to shutdown and restart using the bootable USB installer again, and run Disk Utility from it to check the HDD for errors.
But then, while booted up from the USB (and after running Disk Utility with a normal result):  the computer suddenly turned off and restarted!  And then it rebooted again into installer mode (i.e. running off the bootable USB), and I ran Disk Utility again and ...it happened again!
So what does this tell me?  I am asking all of you for confirmation please.  I am thinking this is a strong indication that whatever the issue is causing the restarts, it is hardware based, as the system was running off the bootable USB at the time, NOT using installed operating system or software.  AND this reminded me of one other instance where the system had rebooted randomly, while I was in SAFE mode.
Would you agree that this is likely now pointing to a hardware issue?  Is power supply the likely culprit?  Or??  (and recalling that repeated AHT have showed nothing...).  Is it worth trying to fix (out of warranty)?
thanks for any insights,
Warren

Answer 1

These instructions must be carried out as an administrator. If you have only one user account, you are the administrator.
This procedure is a diagnostic test. It makes no changes to your data.
Please triple-click anywhere in the line below on this page to select it:
syslog -k Sender kernel -k Message CSeq 'n Cause: -' | tail | awk '/:/{$4=""; print}' | pbcopy
Copy the selected text to the Clipboard by pressing the key combination command-C.
Launch the built-in Terminal application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Terminal in the icon grid.
Paste into the Terminal window by pressing the key combination command-V. I've tested these instructions only with the Safari web browser. If you use another browser, you may have to press the return key after pasting.
Wait for a new line ending in a dollar sign ($) to appear below what you entered.
The output of the command will be automatically copied to the Clipboard. If the command produced no output, the Clipboard will be empty. Paste into a reply to this message.
The Terminal window doesn't show the output. Please don't copy anything from there.