 CGAL 5.4.1 - CGAL and Solvers

Concepts that describe various solvers.

## Concepts

conceptDiagonalizeTraits< FT, dim >
Concept providing functions to extract eigenvectors and eigenvalues from covariance matrices represented by an array a, using symmetric diagonalization. More...

conceptLinearProgramTraits
A concept that describes the set of methods used to define and solve a linear programming (lp) problem of the general form:

\begin{eqnarray*} & \mbox{minimize} & \mathbf{q}^{T}\mathbf{x} + r \\ & \mbox{subject to} & \mathbf{l} \leq A\mathbf{x} \leq \mathbf{u} \end{eqnarray*}

in $$n$$ real variables $$\mathbf{x} = (x_0, \ldots, x_{n-1})$$ and $$m$$ constraints. More...

conceptMixedIntegerProgramVariable
MixedIntegerProgramVariable is a concept of a variable in a Mixed Integer Programming (MIP) problem. More...

conceptMixedIntegerProgramLinearConstraint< FT >
MixedIntegerProgramLinearConstraint is a concept of a linear constraint in a Mixed Integer Programming (MIP) problem. More...

conceptMixedIntegerProgramLinearObjective< FT >
MixedIntegerProgramLinearObjective is a concept of the linear objective function in a Mixed Integer Programming (MIP) problem. More...

conceptMixedIntegerProgramTraits< FT >
Concept describing the set of requirements for (constrained or unconstrained) Mixed Integer Programming (MIP) problems. A model of this concept stores the integer variables, linear objective, and linear constraints (if any) and provides a method to solve the problem. More...

conceptNormalEquationSparseLinearAlgebraTraits_d
Concept describing the set of requirements for solving the normal equation $$A^t A X = A^t B$$, $$A$$ being a matrix, $$At$$ its transpose matrix, $$B$$ and $$X$$ being two vectors. More...

A concept that describes the set of methods used to define and solve a quadratic programming (qp) problem of the general form:

\begin{eqnarray*} & \mbox{minimize} & \frac{1}{2}\mathbf{x}^{T}P\mathbf{x} + \mathbf{q}^{T}\mathbf{x} + r \\ & \mbox{subject to} & \mathbf{l} \leq A\mathbf{x} \leq \mathbf{u} \end{eqnarray*}

in $$n$$ real variables $$\mathbf{x} = (x_0, \ldots, x_{n-1})$$ and $$m$$ constraints. More...

conceptSparseLinearAlgebraTraits_d
The concept SparseLinearAlgebraTraits_d is used to solve sparse linear systems A $$\times$$ X = B. More...

conceptSparseLinearAlgebraWithFactorTraits_d
Concept describing the set of requirements for a direct sparse linear system solver with factorization. A model of this concept stores the left-hand matrix (denoted $$A$$) and provides an additional factorization method to solve the system for different right-hand vectors. More...

conceptSvdTraits
The concept SvdTraits describes the linear algebra types and algorithms needed to solve in the least square sense a linear system with a singular value decomposition. More...