OpenCV: Optimization Algorithms

| OpenCV 3.4.2 Open Source Computer Vision

Classes | Enumerations | Functions
Optimization Algorithms
Core functionality

## Classes
class | cv::ConjGradSolver
| This class is used to perform the non-linear non-constrained minimization of a function with known gradient,. More...
class | cv::DownhillSolver
| This class is used to perform the non-linear non-constrained minimization of a function,. More...
class | cv::MinProblemSolver
| Basic interface for all solvers. More...

## Enumerations
enum | cv::SolveLPResult { cv::SOLVELP_UNBOUNDED = -2, cv::SOLVELP_UNFEASIBLE = -1, cv::SOLVELP_SINGLE = 0, cv::SOLVELP_MULTI = 1 }
| return codes for cv::solveLP() function More...

## Functions
int | cv::solveLP (const Mat &Func, const Mat &Constr, Mat &z)
| Solve given (non-integer) linear programming problem using the Simplex Algorithm (Simplex Method). More...

## Detailed Description

The algorithms in this section minimize or maximize function value within specified constraints or without any constraints.

## Enumeration Type Documentation

## ◆ SolveLPResult

enum cv::SolveLPResult

return codes for cv::solveLP() function

Enumerator
SOLVELP_UNBOUNDED | problem is unbounded (target function can achieve arbitrary high values)
SOLVELP_UNFEASIBLE | problem is unfeasible (there are no points that satisfy all the constraints imposed)
SOLVELP_SINGLE | there is only one maximum for target function
SOLVELP_MULTI | there are multiple maxima for target function - the arbitrary one is returned

## Function Documentation

## ◆ solveLP()

int cv::solveLP | ( | const Mat & | Func,
|  | const Mat & | Constr,
|  | Mat & | z
| ) |  |

Solve given (non-integer) linear programming problem using the Simplex Algorithm (Simplex Method).

What we mean here by "linear programming problem" (or LP problem, for short) can be formulated as:

\[\mbox{Maximize } c\cdot x\\ \mbox{Subject to:}\\ Ax\leq b\\ x\geq 0\]

Where \(c\) is fixed `1`-by-`n` row-vector, \(A\) is fixed `m`-by-`n` matrix, \(b\) is fixed `m`-by-`1` column vector and \(x\) is an arbitrary `n`-by-`1` column vector, which satisfies the constraints.

Simplex algorithm is one of many algorithms that are designed to handle this sort of problems efficiently. Although it is not optimal in theoretical sense (there exist algorithms that can solve any problem written as above in polynomial time, while simplex method degenerates to exponential time for some special cases), it is well-studied, easy to implement and is shown to work well for real-life purposes.

The particular implementation is taken almost verbatim from Introduction to Algorithms, third edition by T. H. Cormen, C. E. Leiserson, R. L. Rivest and Clifford Stein. In particular, the Bland's rule http://en.wikipedia.org/wiki/Bland%27s_rule is used to prevent cycling.

Parameters

  Func | This row-vector corresponds to \(c\) in the LP problem formulation (see above). It should contain 32- or 64-bit floating point numbers. As a convenience, column-vector may be also submitted, in the latter case it is understood to correspond to \(c^T\).
  Constr | `m`-by-`n+1` matrix, whose rightmost column corresponds to \(b\) in formulation above and the remaining to \(A\). It should contain 32- or 64-bit floating point numbers.
  z | The solution will be returned here as a column-vector - it corresponds to \(c\) in the formulation above. It will contain 64-bit floating point numbers.

Returns
  One of cv::SolveLPResult