Notations Definitions N total number of variables M total amount of resource i variable index j resource index X decision variable vector $x=\left({x}_{1},\cdots ,{x}_{N}\right)$ ${f}_{i}\left({x}_{i}\right)$ the objective function related to variable ${x}_{i}$ ${g}_{i}\left({x}_{i}\right)$ the derivative function of ${f}_{i}\left({x}_{i}\right)$ , ${g}_{i}\left({x}_{i}\right)=\text{d}{f}_{i}\left({x}_{i}\right)/\text{d}{x}_{i}$ ${k}_{i}\left({x}_{i}\right)$ the derivative function of ${g}_{i}\left({x}_{i}\right)$ , ${k}_{i}\left({x}_{i}\right)=\text{d}{g}_{i}\left({x}_{i}\right)/\text{d}{x}_{i}$ ${h}_{i}\left(\cdot \right)$ the inverse function of ${g}_{i}\left({x}_{i}\right)$ , ${h}_{i}\left(\cdot \right)={g}_{i}^{-1}\left(\cdot \right)$ ${c}_{i,j}$ coefficient of variable i of resource j ${C}_{j}$ available amount of resource j $\lambda$ the Lagrange multiplier vector for the resource constraints $w$ the Lagrange multiplier vector for the variable constraints $v$ the Lagrange multiplier vector for the variable constraints $f\left(\cdot \right)$ The objective function vector