Sequential Linear Programming $$\begin{aligned} \text{min}&,F\left(\boldsymbol{x}\right)\\ \text{s.t.}&,\begin{cases} {G_j\left(\boldsymbol{x}\right)\le 0}\\ {L_i\le x_i\le U_i} \end{cases} \end{aligned}$$ Generate subproblem below with Taylor expansion to the first order term, and solve it until match convergence criteria. $$\begin{aligned} \text{min}&,F\left(\boldsymbol{x}^k\right)+\nabla F\left(\boldsymbol{x}^k\right)\cdot\Delta \boldsymbol{x}\\ \text{s.t.}&,\begin{cases} {G_j\left(\boldsymbol{x}^k\right)+\nabla G_j\left(\boldsymbol{x}^k\right)\cdot\Delta \boldsymbol{x}\le 0}\\ {\text{max}\left(L_i-x^k_i,-\text{move}\right)\le\Delta x_i\le\text{min}\left(U_i-x^k_i,\text{move}\right)} \end{cases} \end{aligned}$$