Semi Multiplication :

Multiplication is summation in semi log scale. We can take the logarithm when we are optimizing multiplication of variables to convert optimization of summation of terms. It is possible to convert wise versa. Taking exponent of summation of terms we can convert multiplication of terms.
We can express exponantial function using taylor series. 1+x+x^2/2 ... . How about taking half of exponential function. where ,exp^-1() = log , exp^1 = exp , exp^0 = x ,exp^1/2 = semiexp().
So we can define a operator which is between summation (+) and multiplication(x) , this new operator (+x+) can be used in optimization as well.
I also need to emphasis summation and multiplication is and , or operation in logic. But there are some cases between and , or . This is similar to (+x+) operator.
Let me search a little bit.