dest = min(source)
The minss, minsd, minps, and minpd instructions computes the minimum of the source and the destination and store the result(s) in the destination operand. There are also vminss, vminsd, vminps, and vminpd on CPUs with AVX instructions which can compute multiple values at once. Behaviorally these instructions are similar to the various add instructions should you wish to see more details.
minss xmm0, xmm1 ; xmm0 gets 32 bit min of xmm1
minsd xmm0, [x] ; xmm0 gets 64 bit min of x
minps xmm0, [rdi] ; xmm0 gets 4 32 bit mins of [rdi]
minpd xmm0, [x+4*rcx] ; xmm0 gets 2 64 bit mins of array x
vminps xmm3, xmm4, xmm15 ; xmm3 gets 4 32 bit mins of xmm4 & xmm15
vminps ymm3, ymm4, ymm15 ; ymm3 gets 8 32 bit mins of ymm4 & ymm15
vminpd ymm3, ymm5, [x] ; ymm3 gets 4 64 bit mins of ymm5 & array x