Local optimizations improve code within basic blocks. Although the separation is somewhat hazy, we won't include as a local optimization anything that moves code outside a block or uses information from outside a block.
In a sense, this category is redundant. Almost all local optimizations have their global counterpart. The method of detection is often different, however.
Local Common Subexpression Elimination
Local Common Strength Reduction
Local Constant Propagation and Folding