# NonLinearProblems

NonLinear Problems Group

 $\mathbf {f(x) \to min,\ max}$ subjected to $\mathbf{lb} \le \mathbf{x} \le \mathbf{ub}$ $\mathbf{A x} \le \mathbf{b}$ $\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}$ $\mathbf{\forall i=0,...,I: c_i(x) \le 0}$ $\mathbf{\forall j=0,...,J: h_j(x) = 0}$ $\mathbf{ \{ {f, c_i, h_j :R^n \to R \} \subset C^1}}$ (smooth differentiable functions) $\mathbf{x \in R^n}$ $\mathbf {f(x) \to min,\ max}$ subjected to $\mathbf{lb} \le \mathbf{x} \le \mathbf{ub}$ $\mathbf{A x} \le \mathbf{b}$ $\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}$ $\mathbf{\forall i=0,...,I: c_i(x) \le 0}$ $\mathbf{\forall j=0,...,J: h_j(x) = 0}$ $\mathbf{ \{ {f, c_i, h_j :R^n \to R \} \subset C^0}}$ (continuous functions, sometimes with some numerical noise) $\mathbf{x \in R^n}$ $\mathbf {f(x) \to min,\ max\ \ }$(global) subjected to $\mathbf{lb} \le \mathbf{x} \le \mathbf{ub}$ $\mathbf{A x} \le \mathbf{b}$ $\mathbf{\forall i=0,...,I: c_i(x) \le 0}$ $\mathbf{\forall j=0,...,J: h_j(x) = 0}$ $\mathbf{ f, c_i, h_j :R^n \to R }$ $\mathbf{x \in R^n}$ Solve system of non-linear equations $\mathbf{F(x)=0}$ subjected to $\mathbf{lb} \le \mathbf{x} \le \mathbf{ub}$ $\mathbf{A x} \le \mathbf{b}$ $\mathbf{\forall i=0,...,I: c_i(x) \le 0}$ $\mathbf{F: R^n \to R^n}$ $\mathbf{x \in R^n}$ $\mathbf {\sum_{k=0}^{K} f_k(x)^2 \to min}$ subjected to $\mathbf{lb} \le \mathbf{x} \le \mathbf{ub}$ $\mathbf{A x} \le \mathbf{b}$ $\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}$ $\mathbf{\forall i=0,...,I: c_i(x) \le 0}$ $\mathbf{\forall j=0,...,J: h_j(x) = 0}$ $\mathbf{ \{ {f_k, c_i, h_j :R^n \to R \} \subset C^1}}$ (smooth differentiable functions) $\mathbf{x \in R^n}$ $\mathbf {\sum_{k=0}^{K} \|f(x, X_k)-Y_k\| ^2 \to min}$ subjected to $\mathbf{lb} \le \mathbf{x} \le \mathbf{ub}$ $\mathbf{A x} \le \mathbf{b}$ $\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}$ $\mathbf{\forall i=0,...,I: c_i(x) \le 0}$ $\mathbf{\forall j=0,...,J: h_j(x) = 0}$ $\mathbf{f, c_i, h_j :R^n \to R}$ $\mathbf{x \in R^n,\ X_k \in R^m, Y_k \in R^s}$ $\mathbf{max_{k=0,...,K}\{f_k(x)\} \to min}$ subjected to $\mathbf{lb} \le \mathbf{x} \le \mathbf{ub}$ $\mathbf{A x} \le \mathbf{b}$ $\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}$ $\mathbf{\forall i=0,...,I: c_i(x) \le 0}$ $\mathbf{\forall j=0,...,J: h_j(x) = 0}$ $\mathbf{ \{ {f, c_i, h_j :R^n \to R \} \subset C^1}}$ (smooth differentiable functions) $\mathbf{x \in R^n}$ $\mathbf {f(x) \to min,\ max}$ subjected to $\mathbf{lb} \le \mathbf{x} \le \mathbf{ub}$ $\mathbf{A x} \le \mathbf{b}$ $\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}$ $\mathbf{\forall i=0,...,I: c_i(x) \le 0}$ $\mathbf{\forall j=0,...,J: h_j(x) = 0}$ $\mathbf{\forall k \in \{k_1,k_2,...k_m\}: x_k \in S_k}$ $\mathbf{S_k\ is\ a\ set\ of\ values\ from\ R}$ $\mathbf{ \{ {f, c_i, h_j :R^n \to R \} \subset C^1}}$ (smooth differentiable functions) $\mathbf{x \in R^n}$ \begin{align} \vec f(\vec x) \to \vec F \\ \text{subjected to} \\ \vec g(\vec x) & \le \vec 0 \\ \vec h(\vec x) & = \vec 0 \\ \vec x_l \le & \vec x \le \vec x_u \\ \vec x \in & R^n \\ \vec f: R^n \to R^m\\ \vec F \in (R \cup \{-\infty,\infty\})^m\\ \end{align}
##### Latest OOSuite 0.38

from 2012-03-15

2012-06-15

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