About Install Documentation Problems Tree Forum Save your money
via IT outsourcing!
Ukrainian HI-TECH Initiative

MatrixProblems

From OpenOpt

Jump to: navigation, search
Matrix Problems Group


\mathbf{f^T x \to min,\ max}
subjected to
\mathbf{lb \le x \le ub}
\mathbf{A x \le b}
\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}
\mathbf{f^T x \to min,\ max}
subjected to
\mathbf{lb \le x \le ub}
\mathbf{A x \le b}
\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}
\forall \mathbf{i} \in \mathbf{intVars}: \mathbf{x_i} \in \mathbf{Z}
\forall \mathbf{j} \in \mathbf{boolVars}: \mathbf{x_j} \in \{0,1\}
\frac{1}{2}\mathbf{x}^T\mathbf{Hx} + \mathbf{f}^T \mathbf{x \rightarrow 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}
\frac{1}{2} \mathbf{\| C x - d \|^2} + \frac{1}{2} \mathbf{\mu \| x - \widehat{x} \|^2 \rightarrow 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{f^T x \to min}
subjected to
\mathbf{lb \le x \le ub}
\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}
\mathbf{\forall i = 0,\dots,I: \lVert C_i x + d_i \rVert_2 \leq q_i^T x + s_i}
x,\ f \in \mathbb{R}^n
C_i \in \mathbb{R}^{{m_i}\times n}, \ d_i \in \mathbb{R}^{m_i}
q_i \in \mathbb{R}^n, \ s_i \in \mathbb{R}
A_{eq} \in \mathbb{R}^{p_{eq}\times n}, \ b_{eq} \in \mathbb{R}^{p_{eq}}
\mathbf{f^T x \to min}
subjected to
\mathbf{lb \le x \le ub}
\mathbf{A x \le b}
\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}
\mathbf{\forall i = 0,...,I: \sum_{j=0}^{n-1} S^{ij} x_j \le d^i}
(matrix componentwise inequalities)
\mathbf{x \in R^n;\ S^{ij}, d^i \in R^{m_i \times m_i}}
\mathbf{i = 0,...,I;\ j = 0,...,n-1}
\mathbf{S^{ij}} are positive semidefinite matrices

(aka LLADP - Linear Least Absolute Deviation Problem)

\mathbf{\| C x - d \|_1} + \mathbf{\mu \| x - \widehat{x} \|_1 \rightarrow min}
subjected to
\mathbf{lb} \le \mathbf{x} \le \mathbf{ub}
\mathbf{\| C x - d \|_{\infty} (= max |C x - d|) \rightarrow 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}
Retrieved from "http://openopt.org/MatrixProblems"
Personal tools
Latest OOSuite 0.29