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AbstractProblemFormulation


Files

file  Residuals.h
file  Variables.h

Classes

class  Data
class  LinearSystem
class  ProblemFormulation
class  Residuals
class  Variables

Detailed Description

Abstract base classes for defining a problem formulation.

A quadratic program QP takes the form

 minimize    c'* x + (1/2) * x' * Q * x
 subject to  A x  = b
             C x >= d

However, for many (possibly most) QP's, the matrices in the formulation have structure that may be exploited to solve the problem more efficiently. The AbstractProblemFormulation module contains abstract base classes upon which these specialized formulations are based. The optimality conditions of the simple QP defined above as are follows:

 rQ  = c + Q * x - A' * y - C' * z = 0
 rA  = A * x - b                   = 0
 rC  = C * x - s - d               = 0
 r3  = S * z                       = 0
 s, z >= 0

Where rQ, rA, rC and r3 newly defined quantities known as residual vectors and x, y, z and s are variables of used in the solution of the QPs.


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