The good news is that you can probably very easily recover from your mistake. The bad news is that the recovery will likely wipe out your VPS (requiring you to have to make a backup of your site onto your computer and, depending on what version of Plesk is installed and your allowed options, either restore the VPS yourself or have your host do it).

Here is the problem:

Virtual Private Servers (VPS) are not the same as Virtual Machines (VM) even though they are very similar. In a full VM, you have a physical server, a piece of software known as a type-I hypervisor, followed by a virtually installed operating system. You know what a physical server is obviously. A type-I hypervisor (in a nutshell) is basically a set if instructions that take the hardware on the server and presents it virtually so that multiple "guest" systems can utilize the hardware. Lastly, you have the virtualized operating system which includes virtualized drivers and such. In a sense, a VM is a physical machine operating virtually (known as DOM1) rather than operating directly on the physical hardware (DOM0). A VPS, however, you have a physical server, a type-II hypervisor, and then a paravirtualized operating system. The differences here are the type-II hypervisor and the paravirtualized operating system. With a VPS, a type-II hypervisor is an operating system in itself that is running a virtualized abstraction layer. All this means is that you have a OS that is running an application (similar to VMWare Workstation). However, from there, you have a paravirtualized operating system. This means that the OS that you install virtually "borrows" key pieces and elements from the host (so as to not have to use virtualized drivers). The benefit here is that you get a speed boost, which is highly noticeable if you are dealing with a type-I hypervisor (such as Xen) and not so much when you are dealing with a type-II hypervisor (such as Virtuozzo).

So, I said all of that above to say this... in a Virtuozzo environment, while your VPS is private from other VPS's on the physical server, each VPS share certain pieces of code from the main OS running the physical server (they are not fully separate). This means that if you run certain commands from your VPS (commands that do not normally cause damage on a normal dedicated server), you can actually break functions within the VPS, causing it not to work correctly. That's the Virtuozzo part (I'll explain why I mentioned this in just a second). The second part of this is that you have Plesk installed, which is a full web-server control panel. Likewise, running certain commands from your VPS will break Plesk, causing a lot of your web server applications to not work correctly. So here are your mistakes:

1. First, you ran a yum update mod_php. This command merely updates the PHP module and not the full PHP application. You would normally run a yum update php to update php and everything associated with it.

2. You changed values in mySQL so that yum would detect it being out of date.

3. You installed Zend Optimizer on Plesk manually.

4. You ran a yum update, which not only updates outdated applications, it also updates critical system files (some of these files are not actually present on the VPS because of the code sharing I mentioned above).

What you should have done:

1. Asked your web hosting provider to upgrade Plesk for you, which would have upgraded all of your software.

Getting back to the full control panel thing, Plesk actually installs custom versions of programs like Apache, PHP, mySQL, etc. However, when you run yum, you are in a sense, installing the default prepackaged versions of the applications and/or updating the Plesk versions of the applications to the prepackaged ones. For Plesk, this can create problems as it tends to break a lot of things in Plesk (the only commercial panel that I know of in which this does not happen is DirectAdmin, mainly because DirectAdmin installs the prepackaged versions of the software via applications like yum). This is even more dangerous when you are sitting on top of Virtuozzo. I would highly suggest that before you run any kind of upgrade or update program, you do a quick Google search to see if other people with your version of Plesk and Virtuozzo have run into any incompatibilities.