JPEGOptim is a free Linux and Windows program that optimizes the compression of JPG images. It was developed by Timo Kokkonen and first released in 1996. The program has several options, most of which require a basic understanding of image formats and compression, but the default options will almost always yield better results that a typical graphic program. The program can be run to optimize the Huffman tables (and retain the original quality), or re-encode the image at a higher compression level, and lose quality.
To use the program with its default settings, simply drag and drop an image onto the jpegoptim.exe file.
I found this program in the late-2010s while looking for a JPEG equivalent of PNGOut. I use it for all the images I upload to my web site and for large graphic projects I've done.
Although the developer is still adding to the program, he unfortunately developer doesn't maintain builds, even for simpler platforms like Windows, so you have to compile the program from source to get the latest version, although SourceForge still has older binaries available.