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.