Optimization: Capabilities MOSAICmodeling can formulate mixed-integer nonlinear programming (MINLP) problems:
![\min_{u,y} f(x,u,y) \\[1ex] \mathrm{s.\,t.\,} g(x,u,y) = 0, \\ \phantom{\mathrm{s.\,t.\,}} x^\mathrm{L} \leq x \leq x^\mathrm{U}, \\ \phantom{\mathrm{s.\,t.\,}} u^\mathrm{L} \leq u \leq u^\mathrm{U}, \\ \phantom{\mathrm{s.\,t.\,}} y \in \mathcal{Z}^n, \\ \phantom{\mathrm{s.\,t.\,}} y^L \leq y \leq y^U.](https://s0.wp.com/latex.php?latex=+++%5Cmin_%7Bu%2Cy%7D+f%28x%2Cu%2Cy%29+%5C%5C%5B1ex%5D++%5Cmathrm%7Bs.%5C%2Ct.%5C%2C%7D+g%28x%2Cu%2Cy%29+%3D+0%2C+%5C%5C++%5Cphantom%7B%5Cmathrm%7Bs.%5C%2Ct.%5C%2C%7D%7D+x%5E%5Cmathrm%7BL%7D+%5Cleq+x+%5Cleq+x%5E%5Cmathrm%7BU%7D%2C+%5C%5C++%5Cphantom%7B%5Cmathrm%7Bs.%5C%2Ct.%5C%2C%7D%7D+u%5E%5Cmathrm%7BL%7D+%5Cleq+u+%5Cleq+u%5E%5Cmathrm%7BU%7D%2C+%5C%5C++%5Cphantom%7B%5Cmathrm%7Bs.%5C%2Ct.%5C%2C%7D%7D+y+%5Cin+%5Cmathcal%7BZ%7D%5En%2C+%5C%5C++%5Cphantom%7B%5Cmathrm%7Bs.%5C%2Ct.%5C%2C%7D%7D+y%5EL+%5Cleq+y+%5Cleq+y%5EU.+++&bg=ffffff&fg=000000&s=0 "\min_{u,y} f(x,u,y) \\[1ex] \mathrm{s.\,t.\,} g(x,u,y) = 0, \\ \phantom{\mathrm{s.\,t.\,}} x^\mathrm{L} \leq x \leq x^\mathrm{U}, \\ \phantom{\mathrm{s.\,t.\,}} u^\mathrm{L} \leq u \leq u^\mathrm{U}, \\ \phantom{\mathrm{s.\,t.\,}} y \in \mathcal{Z}^n, \\ \phantom{\mathrm{s.\,t.\,}} y^L \leq y \leq y^U.")
