Finding the second largest value In an Array
Several comments are unnecessary:

    // Loop over the array
    for (int i = 0; i &lt; array.length; i++) {

    // assign second highest element to highest element
    secondHighest = highest;


I recommend do use braces { ... } for all if-blocks, even if that
consists only of a single statement, and definitely if there is
an additional comment line:

        } else if (array[i] &gt; secondHighest)
            // Just replace the second highest
            secondHighest = array[i];


Iteration over all array elements can be simplified with an
“enhanced for loop:”

    for (int elem : array) {
        // ...
    }


Your function returns Integer.MIN_VALUE for an empty or single-element
array, which is fine if specified as such. An alternative would be
to throw an exception for arrays with less than two elements.

With respect to performance, I doubt there is much to improve.
The function iterates once over all array elements, which looks pretty
much optimal.